[N,k,chi] = [7500,2,Mod(1,7500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7500, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7500.1");
S:= CuspForms(chi, 2);
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
\(2\)
\(-1\)
\(3\)
\(1\)
\(5\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{7}^{4} - 4T_{7}^{3} - 4T_{7}^{2} + 11T_{7} + 1 \)
T7^4 - 4*T7^3 - 4*T7^2 + 11*T7 + 1
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7500))\).
$p$
$F_p(T)$
$2$
\( T^{4} \)
T^4
$3$
\( (T + 1)^{4} \)
(T + 1)^4
$5$
\( T^{4} \)
T^4
$7$
\( T^{4} - 4 T^{3} - 4 T^{2} + 11 T + 1 \)
T^4 - 4*T^3 - 4*T^2 + 11*T + 1
$11$
\( T^{4} + T^{3} - 24 T^{2} + 46 T - 19 \)
T^4 + T^3 - 24*T^2 + 46*T - 19
$13$
\( T^{4} - 5 T^{3} - 10 T^{2} + 60 T - 45 \)
T^4 - 5*T^3 - 10*T^2 + 60*T - 45
$17$
\( T^{4} - 4 T^{3} - 4 T^{2} + 21 T - 9 \)
T^4 - 4*T^3 - 4*T^2 + 21*T - 9
$19$
\( T^{4} + 5 T^{3} - 5 T^{2} - 15 T + 5 \)
T^4 + 5*T^3 - 5*T^2 - 15*T + 5
$23$
\( T^{4} - 9 T^{3} - 14 T^{2} + 126 T + 171 \)
T^4 - 9*T^3 - 14*T^2 + 126*T + 171
$29$
\( T^{4} - 6 T^{3} + 6 T^{2} + 9 T + 1 \)
T^4 - 6*T^3 + 6*T^2 + 9*T + 1
$31$
\( T^{4} - 11 T^{3} - 34 T^{2} + \cdots + 981 \)
T^4 - 11*T^3 - 34*T^2 + 354*T + 981
$37$
\( T^{4} - 2 T^{3} - 66 T^{2} + \cdots + 1021 \)
T^4 - 2*T^3 - 66*T^2 + 67*T + 1021
$41$
\( T^{4} - 130 T^{2} - 160 T + 2705 \)
T^4 - 130*T^2 - 160*T + 2705
$43$
\( T^{4} + 6 T^{3} - 19 T^{2} - 64 T + 131 \)
T^4 + 6*T^3 - 19*T^2 - 64*T + 131
$47$
\( T^{4} - 16 T^{3} - 14 T^{2} + \cdots - 4099 \)
T^4 - 16*T^3 - 14*T^2 + 1149*T - 4099
$53$
\( T^{4} + 2 T^{3} - 76 T^{2} - 177 T - 99 \)
T^4 + 2*T^3 - 76*T^2 - 177*T - 99
$59$
\( T^{4} - T^{3} - 159 T^{2} - 211 T + 3701 \)
T^4 - T^3 - 159*T^2 - 211*T + 3701
$61$
\( T^{4} + 22 T^{3} + 4 T^{2} + \cdots - 7909 \)
T^4 + 22*T^3 + 4*T^2 - 2022*T - 7909
$67$
\( T^{4} - 36 T^{3} + 421 T^{2} + \cdots - 639 \)
T^4 - 36*T^3 + 421*T^2 - 1536*T - 639
$71$
\( T^{4} - 20 T^{3} + 120 T^{2} - 215 T + 5 \)
T^4 - 20*T^3 + 120*T^2 - 215*T + 5
$73$
\( T^{4} - 12 T^{3} - 61 T^{2} - 38 T + 11 \)
T^4 - 12*T^3 - 61*T^2 - 38*T + 11
$79$
\( T^{4} + 3 T^{3} - 146 T^{2} + \cdots - 639 \)
T^4 + 3*T^3 - 146*T^2 - 918*T - 639
$83$
\( T^{4} - 14 T^{3} - 224 T^{2} + \cdots - 6849 \)
T^4 - 14*T^3 - 224*T^2 + 3486*T - 6849
$89$
\( T^{4} + 15 T^{3} - 150 T^{2} + \cdots - 9875 \)
T^4 + 15*T^3 - 150*T^2 - 3000*T - 9875
$97$
\( T^{4} + 12 T^{3} - 206 T^{2} + \cdots - 8019 \)
T^4 + 12*T^3 - 206*T^2 - 3132*T - 8019
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