[N,k,chi] = [10,18,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 18);
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 \(\beta = 240\sqrt{2941}\).
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
\(2\)
\(-1\)
\(5\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} - 17628T_{3} - 91715004 \)
T3^2 - 17628*T3 - 91715004
acting on \(S_{18}^{\mathrm{new}}(\Gamma_0(10))\).
$p$
$F_p(T)$
$2$
\( (T - 256)^{2} \)
(T - 256)^2
$3$
\( T^{2} - 17628 T - 91715004 \)
T^2 - 17628*T - 91715004
$5$
\( (T + 390625)^{2} \)
(T + 390625)^2
$7$
\( T^{2} + \cdots + 189284738539204 \)
T^2 - 27684196*T + 189284738539204
$11$
\( T^{2} - 64515264 T - 13\!\cdots\!76 \)
T^2 - 64515264*T - 1398138384764030976
$13$
\( T^{2} - 2895838468 T + 11\!\cdots\!56 \)
T^2 - 2895838468*T + 1143891006673316356
$17$
\( T^{2} - 1580212596 T - 32\!\cdots\!96 \)
T^2 - 1580212596*T - 328916388558611941596
$19$
\( T^{2} - 44213712760 T - 82\!\cdots\!00 \)
T^2 - 44213712760*T - 8200400373946680086000
$23$
\( T^{2} - 487549782828 T - 33\!\cdots\!04 \)
T^2 - 487549782828*T - 33069024295086547794204
$29$
\( T^{2} - 3987314863500 T + 39\!\cdots\!00 \)
T^2 - 3987314863500*T + 3973533922215204875460900
$31$
\( T^{2} + 5492261339336 T + 71\!\cdots\!24 \)
T^2 + 5492261339336*T + 7143957929125063164580624
$37$
\( T^{2} + 62715287637884 T + 94\!\cdots\!64 \)
T^2 + 62715287637884*T + 940395427079330782643400964
$41$
\( T^{2} - 23411477277324 T - 41\!\cdots\!56 \)
T^2 - 23411477277324*T - 4141387407423468598739419356
$43$
\( T^{2} + 124856923191092 T + 24\!\cdots\!16 \)
T^2 + 124856923191092*T + 2491905498718098166311287716
$47$
\( T^{2} + 185946612123564 T + 45\!\cdots\!24 \)
T^2 + 185946612123564*T + 4538352835873155273333617124
$53$
\( T^{2} - 359339780647668 T - 74\!\cdots\!44 \)
T^2 - 359339780647668*T - 74769548849251855181632442844
$59$
\( T^{2} - 902179170360600 T - 51\!\cdots\!00 \)
T^2 - 902179170360600*T - 513699494013966676024397804400
$61$
\( T^{2} + \cdots - 87\!\cdots\!56 \)
T^2 + 1564422918967676*T - 872157658650230283742050620156
$67$
\( T^{2} + \cdots + 83\!\cdots\!64 \)
T^2 + 5839738931054684*T + 8356721597053017160538752791364
$71$
\( T^{2} + 67588560434136 T - 91\!\cdots\!76 \)
T^2 + 67588560434136*T - 9193333713607724760386651185776
$73$
\( T^{2} + \cdots - 46\!\cdots\!44 \)
T^2 - 3533390699585668*T - 4681838973617685602203237678844
$79$
\( T^{2} + \cdots + 69\!\cdots\!00 \)
T^2 - 19002656396552080*T + 69570819227028498307177201499200
$83$
\( T^{2} + \cdots - 90\!\cdots\!64 \)
T^2 - 21675087975118188*T - 90077162589151917360491107339164
$89$
\( T^{2} + \cdots + 20\!\cdots\!00 \)
T^2 + 97499522192222220*T + 2050169847694470065929134294872100
$97$
\( T^{2} + \cdots + 23\!\cdots\!84 \)
T^2 - 99889937855386756*T + 2338852271533590189216302936090884
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