[N,k,chi] = [2300,4,Mod(1,2300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2300, 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("2300.1");
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
\(2\)
\(-1\)
\(5\)
\(1\)
\(23\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{3} - 4T_{3}^{2} - 17T_{3} + 24 \)
T3^3 - 4*T3^2 - 17*T3 + 24
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(2300))\).
$p$
$F_p(T)$
$2$
\( T^{3} \)
T^3
$3$
\( T^{3} - 4 T^{2} - 17 T + 24 \)
T^3 - 4*T^2 - 17*T + 24
$5$
\( T^{3} \)
T^3
$7$
\( T^{3} - 46 T^{2} + 196 T + 6416 \)
T^3 - 46*T^2 + 196*T + 6416
$11$
\( T^{3} + 64 T^{2} - 1112 T - 88184 \)
T^3 + 64*T^2 - 1112*T - 88184
$13$
\( T^{3} - 44 T^{2} - 1739 T + 3334 \)
T^3 - 44*T^2 - 1739*T + 3334
$17$
\( T^{3} - 88 T^{2} - 17920 T + 1617496 \)
T^3 - 88*T^2 - 17920*T + 1617496
$19$
\( T^{3} + 94 T^{2} - 9364 T - 184984 \)
T^3 + 94*T^2 - 9364*T - 184984
$23$
\( (T - 23)^{3} \)
(T - 23)^3
$29$
\( T^{3} - 308 T^{2} + 30877 T - 1008698 \)
T^3 - 308*T^2 + 30877*T - 1008698
$31$
\( T^{3} + 140 T^{2} - 66217 T - 1074768 \)
T^3 + 140*T^2 - 66217*T - 1074768
$37$
\( T^{3} + 26 T^{2} - 88484 T + 4672784 \)
T^3 + 26*T^2 - 88484*T + 4672784
$41$
\( T^{3} - 584 T^{2} + \cdots + 21405186 \)
T^3 - 584*T^2 + 19753*T + 21405186
$43$
\( T^{3} - 478 T^{2} + \cdots + 14441984 \)
T^3 - 478*T^2 + 4704*T + 14441984
$47$
\( T^{3} - 28 T^{2} - 199601 T + 25906224 \)
T^3 - 28*T^2 - 199601*T + 25906224
$53$
\( T^{3} + 356 T^{2} - 116276 T - 63184 \)
T^3 + 356*T^2 - 116276*T - 63184
$59$
\( T^{3} - 144 T^{2} + \cdots - 15495744 \)
T^3 - 144*T^2 - 157376*T - 15495744
$61$
\( T^{3} + 1052 T^{2} + \cdots - 55378432 \)
T^3 + 1052*T^2 + 141172*T - 55378432
$67$
\( T^{3} - 2008 T^{2} + \cdots - 228170232 \)
T^3 - 2008*T^2 + 1249512*T - 228170232
$71$
\( T^{3} - 360 T^{2} - 38189 T + 7542816 \)
T^3 - 360*T^2 - 38189*T + 7542816
$73$
\( T^{3} - 252 T^{2} + \cdots - 34560066 \)
T^3 - 252*T^2 - 323855*T - 34560066
$79$
\( T^{3} + 720 T^{2} + \cdots - 932658192 \)
T^3 + 720*T^2 - 1198556*T - 932658192
$83$
\( T^{3} - 1404 T^{2} + \cdots + 464610136 \)
T^3 - 1404*T^2 - 59336*T + 464610136
$89$
\( T^{3} - 534 T^{2} + \cdots + 77599776 \)
T^3 - 534*T^2 - 1225976*T + 77599776
$97$
\( T^{3} + 736 T^{2} + \cdots - 67270584 \)
T^3 + 736*T^2 - 584152*T - 67270584
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