[N,k,chi] = [240,10,Mod(1,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("240.1");
S:= CuspForms(chi, 10);
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
sage: f.q_expansion() # note that sage often uses an isomorphic number field
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 4\sqrt{4729}\).
We also show the integral \(q\)-expansion of the trace form .
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
\( T_{7}^{2} - 11872T_{7} + 31528560 \)
T7^2 - 11872*T7 + 31528560
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(240))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( (T + 81)^{2} \)
(T + 81)^2
$5$
\( (T + 625)^{2} \)
(T + 625)^2
$7$
\( T^{2} - 11872 T + 31528560 \)
T^2 - 11872*T + 31528560
$11$
\( T^{2} + 35488 T - 4189882368 \)
T^2 + 35488*T - 4189882368
$13$
\( T^{2} - 143676 T + 2896150388 \)
T^2 - 143676*T + 2896150388
$17$
\( T^{2} - 385156 T + 31364196084 \)
T^2 - 385156*T + 31364196084
$19$
\( T^{2} - 403296 T + 39554119280 \)
T^2 - 403296*T + 39554119280
$23$
\( T^{2} + 223704 T - 4977578430720 \)
T^2 + 223704*T - 4977578430720
$29$
\( T^{2} + 74572 T - 180861933660 \)
T^2 + 74572*T - 180861933660
$31$
\( T^{2} - 5027128 T - 463313088000 \)
T^2 - 5027128*T - 463313088000
$37$
\( T^{2} - 5373628 T - 28861754638220 \)
T^2 - 5373628*T - 28861754638220
$41$
\( T^{2} + \cdots - 210775232832060 \)
T^2 - 14211332*T - 210775232832060
$43$
\( T^{2} + \cdots + 165047750825744 \)
T^2 + 27748920*T + 165047750825744
$47$
\( T^{2} + 95966440 T + 20\!\cdots\!76 \)
T^2 + 95966440*T + 2082398270597376
$53$
\( T^{2} + 64305596 T + 11555844938820 \)
T^2 + 64305596*T + 11555844938820
$59$
\( T^{2} + 187863136 T + 57\!\cdots\!60 \)
T^2 + 187863136*T + 5745641782978560
$61$
\( T^{2} - 154080060 T - 85608279866044 \)
T^2 - 154080060*T - 85608279866044
$67$
\( T^{2} + 33592376 T - 65\!\cdots\!56 \)
T^2 + 33592376*T - 65232884349014256
$71$
\( T^{2} - 228270976 T - 45\!\cdots\!56 \)
T^2 - 228270976*T - 45919384536416256
$73$
\( T^{2} + 33122316 T - 49\!\cdots\!00 \)
T^2 + 33122316*T - 49372065464527900
$79$
\( T^{2} - 932406760 T + 21\!\cdots\!00 \)
T^2 - 932406760*T + 213523438937692800
$83$
\( T^{2} + 207040152 T - 10\!\cdots\!68 \)
T^2 + 207040152*T - 1097200204595568
$89$
\( T^{2} - 224518164 T - 89\!\cdots\!40 \)
T^2 - 224518164*T - 89786907488203740
$97$
\( T^{2} - 387134596 T - 22\!\cdots\!96 \)
T^2 - 387134596*T - 2255431146557740796
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