[N,k,chi] = [930,4,Mod(1,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Newform invariants
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
Refresh table
\( p \)
Sign
\(2\)
\(-1\)
\(3\)
\(1\)
\(5\)
\(1\)
\(31\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{7}^{4} + 3T_{7}^{3} - 1120T_{7}^{2} - 3352T_{7} + 221954 \)
T7^4 + 3*T7^3 - 1120*T7^2 - 3352*T7 + 221954
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(930))\).
$p$
$F_p(T)$
$2$
\( (T - 2)^{4} \)
(T - 2)^4
$3$
\( (T + 3)^{4} \)
(T + 3)^4
$5$
\( (T + 5)^{4} \)
(T + 5)^4
$7$
\( T^{4} + 3 T^{3} - 1120 T^{2} + \cdots + 221954 \)
T^4 + 3*T^3 - 1120*T^2 - 3352*T + 221954
$11$
\( T^{4} - 43 T^{3} - 2290 T^{2} + \cdots - 87048 \)
T^4 - 43*T^3 - 2290*T^2 + 77436*T - 87048
$13$
\( T^{4} + 20 T^{3} - 3038 T^{2} + \cdots - 34740 \)
T^4 + 20*T^3 - 3038*T^2 - 39318*T - 34740
$17$
\( T^{4} + 28 T^{3} - 13232 T^{2} + \cdots - 2335440 \)
T^4 + 28*T^3 - 13232*T^2 - 354228*T - 2335440
$19$
\( T^{4} + 73 T^{3} - 2684 T^{2} + \cdots - 5882560 \)
T^4 + 73*T^3 - 2684*T^2 - 307536*T - 5882560
$23$
\( T^{4} + 47 T^{3} + \cdots + 153604380 \)
T^4 + 47*T^3 - 30946*T^2 - 302424*T + 153604380
$29$
\( T^{4} - 204 T^{3} - 7824 T^{2} + \cdots + 3115368 \)
T^4 - 204*T^3 - 7824*T^2 + 555894*T + 3115368
$31$
\( (T - 31)^{4} \)
(T - 31)^4
$37$
\( T^{4} + 156 T^{3} + \cdots - 1266846400 \)
T^4 + 156*T^3 - 97354*T^2 - 24065170*T - 1266846400
$41$
\( T^{4} - 128 T^{3} + \cdots - 823625856 \)
T^4 - 128*T^3 - 127504*T^2 + 24981024*T - 823625856
$43$
\( T^{4} - 685 T^{3} + \cdots + 5476990600 \)
T^4 - 685*T^3 - 93454*T^2 + 82603940*T + 5476990600
$47$
\( T^{4} - 156 T^{3} + \cdots + 4286240520 \)
T^4 - 156*T^3 - 183956*T^2 + 24990708*T + 4286240520
$53$
\( T^{4} - 591 T^{3} + \cdots + 9055700772 \)
T^4 - 591*T^3 - 242600*T^2 + 129290328*T + 9055700772
$59$
\( T^{4} - 212 T^{3} + \cdots - 1590405900 \)
T^4 - 212*T^3 - 98284*T^2 + 28476174*T - 1590405900
$61$
\( T^{4} - 1288 T^{3} + \cdots - 16176506480 \)
T^4 - 1288*T^3 + 464168*T^2 - 2579776*T - 16176506480
$67$
\( T^{4} - 1270 T^{3} + \cdots - 1068288812 \)
T^4 - 1270*T^3 + 423002*T^2 - 23010514*T - 1068288812
$71$
\( T^{4} - 2465 T^{3} + \cdots + 136879857138 \)
T^4 - 2465*T^3 + 2261252*T^2 - 913561986*T + 136879857138
$73$
\( T^{4} + 359 T^{3} + \cdots + 155582080054 \)
T^4 + 359*T^3 - 1234282*T^2 - 512012932*T + 155582080054
$79$
\( T^{4} - 2053 T^{3} + \cdots - 91345005380 \)
T^4 - 2053*T^3 + 1094264*T^2 + 50745536*T - 91345005380
$83$
\( T^{4} - 994 T^{3} + \cdots + 570567120 \)
T^4 - 994*T^3 + 174340*T^2 + 35969124*T + 570567120
$89$
\( T^{4} - 1055 T^{3} + \cdots + 314857727442 \)
T^4 - 1055*T^3 - 1010998*T^2 + 586797150*T + 314857727442
$97$
\( T^{4} - 2962 T^{3} + \cdots - 1059198695360 \)
T^4 - 2962*T^3 + 1986920*T^2 + 1036764416*T - 1059198695360
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