[N,k,chi] = [304,10,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, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.1");
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
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
\( T_{3}^{4} + 226T_{3}^{3} - 39131T_{3}^{2} - 8791740T_{3} - 337930956 \)
T3^4 + 226*T3^3 - 39131*T3^2 - 8791740*T3 - 337930956
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(304))\).
$p$
$F_p(T)$
$2$
\( T^{4} \)
T^4
$3$
\( T^{4} + 226 T^{3} + \cdots - 337930956 \)
T^4 + 226*T^3 - 39131*T^2 - 8791740*T - 337930956
$5$
\( T^{4} - 866 T^{3} + \cdots + 1852446724000 \)
T^4 - 866*T^3 - 3665655*T^2 + 315628300*T + 1852446724000
$7$
\( T^{4} + \cdots + 786353549326443 \)
T^4 + 2670*T^3 - 61696860*T^2 - 116436017502*T + 786353549326443
$11$
\( T^{4} + 119234 T^{3} + \cdots + 30\!\cdots\!92 \)
T^4 + 119234*T^3 + 2279476197*T^2 - 65933876389888*T + 308126839450989292
$13$
\( T^{4} + 6748 T^{3} + \cdots - 79\!\cdots\!24 \)
T^4 + 6748*T^3 - 21677117661*T^2 - 1303658610803432*T - 7995567793303427024
$17$
\( T^{4} - 678624 T^{3} + \cdots + 16\!\cdots\!09 \)
T^4 - 678624*T^3 - 173140916562*T^2 + 102397547874735072*T + 16770071816538119339409
$19$
\( (T - 130321)^{4} \)
(T - 130321)^4
$23$
\( T^{4} + 2911868 T^{3} + \cdots - 60\!\cdots\!88 \)
T^4 + 2911868*T^3 - 183984048477*T^2 - 2727384504786073504*T - 600122008478848814929088
$29$
\( T^{4} - 8291104 T^{3} + \cdots - 13\!\cdots\!00 \)
T^4 - 8291104*T^3 + 6979347050031*T^2 + 71525180313253109780*T - 134608470516236163811830500
$31$
\( T^{4} + 3445468 T^{3} + \cdots + 16\!\cdots\!44 \)
T^4 + 3445468*T^3 - 29678593269744*T^2 - 31506328044595609280*T + 168619000110536849783110144
$37$
\( T^{4} + 1005524 T^{3} + \cdots + 88\!\cdots\!52 \)
T^4 + 1005524*T^3 - 457850038983408*T^2 - 1470519655424707720528*T + 8866531687708926627598559152
$41$
\( T^{4} - 8514124 T^{3} + \cdots - 18\!\cdots\!92 \)
T^4 - 8514124*T^3 - 733459745449164*T^2 + 7737695987371834315712*T - 18346480403306858802771867392
$43$
\( T^{4} + 13900726 T^{3} + \cdots - 70\!\cdots\!72 \)
T^4 + 13900726*T^3 - 747338384701767*T^2 - 15995022075570608376188*T - 70192106126611993101129318272
$47$
\( T^{4} - 36334954 T^{3} + \cdots + 11\!\cdots\!00 \)
T^4 - 36334954*T^3 - 3143481498548271*T^2 + 99564361128602630437400*T + 1154203026795396307288586972800
$53$
\( T^{4} + 113969356 T^{3} + \cdots - 13\!\cdots\!08 \)
T^4 + 113969356*T^3 - 2536079015140869*T^2 - 587215651565597308430432*T - 13487369796792560586503424791408
$59$
\( T^{4} - 396773766 T^{3} + \cdots - 41\!\cdots\!00 \)
T^4 - 396773766*T^3 + 49363170632995341*T^2 - 1583843431700836199825100*T - 41818269970641448879902199597500
$61$
\( T^{4} + 298192066 T^{3} + \cdots - 32\!\cdots\!92 \)
T^4 + 298192066*T^3 + 21473548273899621*T^2 - 308236570710201138164768*T - 32199441068846684752964131599092
$67$
\( T^{4} - 113551722 T^{3} + \cdots - 45\!\cdots\!48 \)
T^4 - 113551722*T^3 - 58688917279201671*T^2 + 10570164796706513617182096*T - 458278714204757844014880251455248
$71$
\( T^{4} + 4659620 T^{3} + \cdots - 13\!\cdots\!12 \)
T^4 + 4659620*T^3 - 116771198854642560*T^2 - 12907935080980548175132048*T - 138540323272325050161300548202512
$73$
\( T^{4} - 136198452 T^{3} + \cdots + 14\!\cdots\!57 \)
T^4 - 136198452*T^3 - 76284324026492010*T^2 + 5173874176279141940539500*T + 1497631820380355263468759198539057
$79$
\( T^{4} + 67255424 T^{3} + \cdots + 32\!\cdots\!00 \)
T^4 + 67255424*T^3 - 12614020693462548*T^2 - 601322097617278492281760*T + 32645049458281639565016920262400
$83$
\( T^{4} + 1376505216 T^{3} + \cdots + 94\!\cdots\!24 \)
T^4 + 1376505216*T^3 + 658124224934927004*T^2 + 131853604225538063192208480*T + 9411620446980068862064487278060224
$89$
\( T^{4} - 1557211260 T^{3} + \cdots + 42\!\cdots\!00 \)
T^4 - 1557211260*T^3 + 634805908820871600*T^2 - 31987344382092354060936000*T + 427022221817843804142415560960000
$97$
\( T^{4} - 975818188 T^{3} + \cdots - 24\!\cdots\!84 \)
T^4 - 975818188*T^3 + 194682750107261220*T^2 + 20879697755308536758590208*T - 2471473416148740904964391177622784
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