[N,k,chi] = [35,10,Mod(1,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("35.1");
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 \(\beta = 2\sqrt{2}\).
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
\(5\)
\(-1\)
\(7\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{2} + 24T_{2} + 136 \)
T2^2 + 24*T2 + 136
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(35))\).
$p$
$F_p(T)$
$2$
\( T^{2} + 24T + 136 \)
T^2 + 24*T + 136
$3$
\( T^{2} + 174T - 15759 \)
T^2 + 174*T - 15759
$5$
\( (T - 625)^{2} \)
(T - 625)^2
$7$
\( (T - 2401)^{2} \)
(T - 2401)^2
$11$
\( T^{2} - 18566 T - 579804919 \)
T^2 - 18566*T - 579804919
$13$
\( T^{2} + 51090 T - 2036537423 \)
T^2 + 51090*T - 2036537423
$17$
\( T^{2} + 373910 T + 33107255257 \)
T^2 + 373910*T + 33107255257
$19$
\( T^{2} + 143276 T - 2624597308 \)
T^2 + 143276*T - 2624597308
$23$
\( T^{2} + 498908 T - 5335908376796 \)
T^2 + 498908*T - 5335908376796
$29$
\( T^{2} + 11577554 T + 32805350195857 \)
T^2 + 11577554*T + 32805350195857
$31$
\( T^{2} + 3953760 T - 34498247424800 \)
T^2 + 3953760*T - 34498247424800
$37$
\( T^{2} + \cdots - 125243882156764 \)
T^2 + 3205412*T - 125243882156764
$41$
\( T^{2} + \cdots - 857114015266016 \)
T^2 - 1058992*T - 857114015266016
$43$
\( T^{2} + \cdots - 693124389149372 \)
T^2 - 15948180*T - 693124389149372
$47$
\( T^{2} + \cdots + 353683714337753 \)
T^2 - 65501290*T + 353683714337753
$53$
\( T^{2} + 25114688 T - 63398812089856 \)
T^2 + 25114688*T - 63398812089856
$59$
\( T^{2} + 116159208 T - 88\!\cdots\!84 \)
T^2 + 116159208*T - 8852735693923184
$61$
\( T^{2} + 44688544 T - 14\!\cdots\!04 \)
T^2 + 44688544*T - 1496363783503904
$67$
\( T^{2} - 118092496 T - 42\!\cdots\!64 \)
T^2 - 118092496*T - 42869690130352064
$71$
\( T^{2} + 294165824 T - 25\!\cdots\!56 \)
T^2 + 294165824*T - 25277687205600256
$73$
\( T^{2} + 57419332 T - 16\!\cdots\!52 \)
T^2 + 57419332*T - 1639304479840252
$79$
\( T^{2} + 692852854 T + 11\!\cdots\!81 \)
T^2 + 692852854*T + 113526114873283481
$83$
\( T^{2} + 540679928 T + 50\!\cdots\!96 \)
T^2 + 540679928*T + 5013675332241296
$89$
\( T^{2} + 779043704 T + 75\!\cdots\!32 \)
T^2 + 779043704*T + 75907476395176432
$97$
\( T^{2} + 2673039406 T + 17\!\cdots\!09 \)
T^2 + 2673039406*T + 1769590542896321009
show more
show less