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Murmurations of modular form L-functions
Weight 2 newforms for Γ0(N)
| all levels | | squarefree levels |
dimension 1 |
![](w2_0_sum.gif) |
![](w2_0_usum.gif) |
|
![](w2sf_0_sum.gif) |
![](w2sf_0_usum.gif) |
all dimensions |
![](w2_all_sum.gif) |
![](w2_all_usum.gif) |
|
![](w2sf_all_sum.gif) |
![](w2sf_all_usum.gif) |
varying dimension |
![](w2_vary_sum.gif) |
![](w2_vary_usum.gif) |
|
![](w2sf_vary_sum.gif) |
![](w2sf_vary_usum.gif) |
Weight 4 newforms for Γ0(N)
| all levels | | squarefree levels |
dimension 1 |
![](w4_0_sum.gif) |
![](w4_0_usum.gif) |
|
![](w4sf_0_sum.gif) |
![](w4sf_0_usum.gif) |
all dimensions |
![](w4_all_sum.gif) |
![](w4_all_usum.gif) |
|
![](w4sf_all_sum.gif) |
![](w4sf_all_usum.gif) |
varying dimension |
![](w4_vary_sum.gif) |
![](w4_vary_usum.gif) |
|
![](w4sf_vary_sum.gif) |
![](w4sf_vary_usum.gif) |
Weight 6 newforms for Γ0(N)
| all levels | | squarefree levels |
dimension 1 |
![](w6_0_sum.gif) |
![](w6_0_usum.gif) |
|
![](w6sf_0_sum.gif) |
![](w6sf_0_usum.gif) |
all dimensions |
![](w6_all_sum.gif) |
![](w6_all_usum.gif) |
|
![](w6sf_all_sum.gif) |
![](w6sf_all_usum.gif) |
varying dimension |
![](w6_vary_sum.gif) |
![](w6_vary_usum.gif) |
|
![](w6sf_vary_sum.gif) |
![](w6sf_vary_usum.gif) |
Weight k > 6 newforms for Γ0(N)
| all levels | | squarefree levels |
weight 8 |
![](w8_all_sum.gif) |
![](w8_all_usum.gif) |
|
![](w8sf_all_sum.gif) |
![](w8sf_all_usum.gif) |
weight 10 |
![](w10_all_sum.gif) |
![](w10_all_usum.gif) |
|
![](w10sf_all_sum.gif) |
![](w10sf_all_usum.gif) |
weight 12 |
![](w12_all_sum.gif) |
![](w12_all_usum.gif) |
|
![](w12sf_all_sum.gif) |
![](w12sf_all_usum.gif) |
weights 2-12 |
![](wk_all_sum.gif) |
![](wk_all_usum.gif) |
|
![](wksf_all_sum.gif) |
![](wksf_all_usum.gif) |
Murmurations of elliptic curve L-functions
by conductor (LMFDB) |
![](ec_sum.gif) |
![](ec_usum.gif) |
![](ec_lsum.gif) |
by conductor (Stein-Watkins) |
![](ecsw_sum.gif) |
![](ecsw_usum.gif) |
![](ecsw_lsum.gif) |
by squarefree conductor (LMFDB) |
![](ecsf_sum.gif) |
![](ecsf_usum.gif) |
![](ecsf_lsum.gif) |
by naive height |
![](eh_sum.gif) |
![](eh_usum.gif) |
![](eh_lsum.gif) |
by j-invariant |
![](ej_sum.gif) |
![](ej_usum.gif) |
![](ej_lsum.gif) |
by discriminant |
![](ed_sum.gif) |
![](ed_usum.gif) |
![](ed_lsum.gif) |
Murmurations of abelian surface L-functions
generic abelian surfaces |
![](g2c_sum.gif) |
![](g2c_usum.gif) |
![](g2c_lsum.gif) |
SU(2)xSU(2) products of elliptic curves |
![](ecec_sum.gif) |
![](ecec_usum.gif) |
![](ecec_lsum.gif) |
N(SU(2)xSU(2)) |
![](nsusu_sum.gif) |
![](nsusu_usum.gif) |
![](nsusu_lsum.gif) |