[N,k,chi] = [304,4,Mod(1,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, 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("304.1");
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
\(2\)
\(1\)
\(19\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{3} + 4T_{3}^{2} - 43T_{3} - 62 \)
T3^3 + 4*T3^2 - 43*T3 - 62
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(304))\).
$p$
$F_p(T)$
$2$
\( T^{3} \)
T^3
$3$
\( T^{3} + 4 T^{2} - 43 T - 62 \)
T^3 + 4*T^2 - 43*T - 62
$5$
\( T^{3} - 7 T^{2} - 244 T + 608 \)
T^3 - 7*T^2 - 244*T + 608
$7$
\( T^{3} + 7 T^{2} - 89 T - 559 \)
T^3 + 7*T^2 - 89*T - 559
$11$
\( T^{3} + 103 T^{2} + 2212 T - 22156 \)
T^3 + 103*T^2 + 2212*T - 22156
$13$
\( T^{3} - 32 T^{2} - 3677 T + 131420 \)
T^3 - 32*T^2 - 3677*T + 131420
$17$
\( T^{3} - 11 T^{2} - 3417 T - 32173 \)
T^3 - 11*T^2 - 3417*T - 32173
$19$
\( (T - 19)^{3} \)
(T - 19)^3
$23$
\( T^{3} + 316 T^{2} + 23147 T - 242336 \)
T^3 + 316*T^2 + 23147*T - 242336
$29$
\( T^{3} + 138 T^{2} + 419 T - 345766 \)
T^3 + 138*T^2 + 419*T - 345766
$31$
\( T^{3} + 420 T^{2} + 55584 T + 2336256 \)
T^3 + 420*T^2 + 55584*T + 2336256
$37$
\( T^{3} - 102 T^{2} + \cdots + 15565400 \)
T^3 - 102*T^2 - 162852*T + 15565400
$41$
\( T^{3} + 370 T^{2} + 36160 T + 707456 \)
T^3 + 370*T^2 + 36160*T + 707456
$43$
\( T^{3} + 431 T^{2} - 20508 T - 5420480 \)
T^3 + 431*T^2 - 20508*T - 5420480
$47$
\( T^{3} - 199 T^{2} + \cdots + 45306112 \)
T^3 - 199*T^2 - 215112*T + 45306112
$53$
\( T^{3} + 308 T^{2} - 340901 T + 6630640 \)
T^3 + 308*T^2 - 340901*T + 6630640
$59$
\( T^{3} - 188 T^{2} - 2195 T + 1077242 \)
T^3 - 188*T^2 - 2195*T + 1077242
$61$
\( T^{3} + 609 T^{2} + \cdots - 50618548 \)
T^3 + 609*T^2 - 43132*T - 50618548
$67$
\( T^{3} - 246 T^{2} + \cdots + 96246632 \)
T^3 - 246*T^2 - 394447*T + 96246632
$71$
\( T^{3} - 954 T^{2} + \cdots + 237273448 \)
T^3 - 954*T^2 - 168772*T + 237273448
$73$
\( T^{3} + 629 T^{2} + \cdots - 417051529 \)
T^3 + 629*T^2 - 644845*T - 417051529
$79$
\( T^{3} + 452 T^{2} + \cdots - 601611824 \)
T^3 + 452*T^2 - 1027892*T - 601611824
$83$
\( T^{3} - 780 T^{2} + \cdots + 1048786960 \)
T^3 - 780*T^2 - 1404148*T + 1048786960
$89$
\( T^{3} + 1356 T^{2} + \cdots + 71672320 \)
T^3 + 1356*T^2 + 568736*T + 71672320
$97$
\( T^{3} + 548 T^{2} + \cdots - 2035482752 \)
T^3 + 548*T^2 - 2588924*T - 2035482752
show more
show less