[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
\( T_{3}^{3} + 8T_{3}^{2} - 49T_{3} - 284 \)
T3^3 + 8*T3^2 - 49*T3 - 284
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(2300))\).
$p$
$F_p(T)$
$2$
\( T^{3} \)
T^3
$3$
\( T^{3} + 8 T^{2} - 49 T - 284 \)
T^3 + 8*T^2 - 49*T - 284
$5$
\( T^{3} \)
T^3
$7$
\( T^{3} + 42 T^{2} + 452 T + 288 \)
T^3 + 42*T^2 + 452*T + 288
$11$
\( T^{3} - 6 T^{2} - 3636 T + 89424 \)
T^3 - 6*T^2 - 3636*T + 89424
$13$
\( T^{3} + 100 T^{2} + 2021 T - 24394 \)
T^3 + 100*T^2 + 2021*T - 24394
$17$
\( T^{3} - 28 T^{2} - 3360 T + 56376 \)
T^3 - 28*T^2 - 3360*T + 56376
$19$
\( T^{3} - 120 T^{2} + 1652 T - 3984 \)
T^3 - 120*T^2 + 1652*T - 3984
$23$
\( (T + 23)^{3} \)
(T + 23)^3
$29$
\( T^{3} + 128 T^{2} + 453 T - 231174 \)
T^3 + 128*T^2 + 453*T - 231174
$31$
\( T^{3} + 76 T^{2} - 14761 T + 382208 \)
T^3 + 76*T^2 - 14761*T + 382208
$37$
\( T^{3} - 212 T^{2} - 9440 T - 64536 \)
T^3 - 212*T^2 - 9440*T - 64536
$41$
\( T^{3} + 580 T^{2} + 79873 T - 509682 \)
T^3 + 580*T^2 + 79873*T - 509682
$43$
\( T^{3} - 20 T^{2} - 193472 T + 25961472 \)
T^3 - 20*T^2 - 193472*T + 25961472
$47$
\( T^{3} - 396 T^{2} + 10895 T + 5642304 \)
T^3 - 396*T^2 + 10895*T + 5642304
$53$
\( T^{3} - 122 T^{2} + \cdots - 28384056 \)
T^3 - 122*T^2 - 297140*T - 28384056
$59$
\( T^{3} - 632 T^{2} + 66720 T + 9077184 \)
T^3 - 632*T^2 + 66720*T + 9077184
$61$
\( T^{3} - 338 T^{2} + 17516 T + 2020904 \)
T^3 - 338*T^2 + 17516*T + 2020904
$67$
\( T^{3} + 442 T^{2} + \cdots - 105984432 \)
T^3 + 442*T^2 - 606980*T - 105984432
$71$
\( T^{3} - 888 T^{2} + \cdots + 150510312 \)
T^3 - 888*T^2 - 219933*T + 150510312
$73$
\( T^{3} + 376 T^{2} + \cdots - 431656494 \)
T^3 + 376*T^2 - 1043687*T - 431656494
$79$
\( T^{3} - 1540 T^{2} + \cdots - 66491136 \)
T^3 - 1540*T^2 + 641716*T - 66491136
$83$
\( T^{3} + 454 T^{2} + \cdots - 241050384 \)
T^3 + 454*T^2 - 893372*T - 241050384
$89$
\( T^{3} + 810 T^{2} - 122616 T - 178848 \)
T^3 + 810*T^2 - 122616*T - 178848
$97$
\( T^{3} + 1284 T^{2} + \cdots + 22204008 \)
T^3 + 1284*T^2 + 324440*T + 22204008
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