[N,k,chi] = [41,4,Mod(1,41)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(41, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("41.1");
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
\(41\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{7} - T_{2}^{6} - 49T_{2}^{5} + 33T_{2}^{4} + 720T_{2}^{3} - 320T_{2}^{2} - 3200T_{2} + 512 \)
T2^7 - T2^6 - 49*T2^5 + 33*T2^4 + 720*T2^3 - 320*T2^2 - 3200*T2 + 512
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(41))\).
$p$
$F_p(T)$
$2$
\( T^{7} - T^{6} - 49 T^{5} + 33 T^{4} + \cdots + 512 \)
T^7 - T^6 - 49*T^5 + 33*T^4 + 720*T^3 - 320*T^2 - 3200*T + 512
$3$
\( T^{7} - 4 T^{6} - 136 T^{5} + \cdots - 31928 \)
T^7 - 4*T^6 - 136*T^5 + 478*T^4 + 4782*T^3 - 7936*T^2 - 57348*T - 31928
$5$
\( T^{7} - 10 T^{6} - 472 T^{5} + \cdots + 5811008 \)
T^7 - 10*T^6 - 472*T^5 + 3676*T^4 + 74996*T^3 - 362184*T^2 - 4145568*T + 5811008
$7$
\( T^{7} - 48 T^{6} + \cdots + 217277488 \)
T^7 - 48*T^6 - 388*T^5 + 40070*T^4 - 192326*T^3 - 6957748*T^2 + 35805564*T + 217277488
$11$
\( T^{7} - 34 T^{6} + \cdots + 1089373224 \)
T^7 - 34*T^6 - 2508*T^5 + 110814*T^4 - 209482*T^3 - 24094808*T^2 + 22347676*T + 1089373224
$13$
\( T^{7} + 60 T^{6} + \cdots - 1344939417600 \)
T^7 + 60*T^6 - 9704*T^5 - 636240*T^4 + 24746832*T^3 + 1867347392*T^2 - 11148462080*T - 1344939417600
$17$
\( T^{7} + 82 T^{6} + \cdots + 359921618304 \)
T^7 + 82*T^6 - 17372*T^5 - 1533560*T^4 + 33244208*T^3 + 4546607456*T^2 + 80768220352*T + 359921618304
$19$
\( T^{7} - 144 T^{6} + \cdots - 10579181757624 \)
T^7 - 144*T^6 - 26948*T^5 + 4708014*T^4 + 43392270*T^3 - 30947952320*T^2 + 1232568437644*T - 10579181757624
$23$
\( T^{7} - 204 T^{6} + \cdots + 5799910821888 \)
T^7 - 204*T^6 - 18856*T^5 + 4237024*T^4 + 117899456*T^3 - 20336796672*T^2 - 539299833344*T + 5799910821888
$29$
\( T^{7} + \cdots - 503094100381696 \)
T^7 - 68*T^6 - 127576*T^5 + 14211584*T^4 + 3426728976*T^3 - 677360438656*T^2 + 36725787219712*T - 503094100381696
$31$
\( T^{7} + \cdots - 298979937161216 \)
T^7 - 696*T^6 + 164712*T^5 - 11748832*T^4 - 881889472*T^3 + 126754484480*T^2 + 534052076032*T - 298979937161216
$37$
\( T^{7} - 730 T^{6} + \cdots + 58\!\cdots\!16 \)
T^7 - 730*T^6 + 139480*T^5 + 24744068*T^4 - 14647604428*T^3 + 2491458236808*T^2 - 192960213630624*T + 5810127077428416
$41$
\( (T + 41)^{7} \)
(T + 41)^7
$43$
\( T^{7} - 368 T^{6} + \cdots - 43\!\cdots\!36 \)
T^7 - 368*T^6 - 301808*T^5 + 141548080*T^4 + 8181501984*T^3 - 10582056704640*T^2 + 1380943189365248*T - 43272910337652736
$47$
\( T^{7} + 26 T^{6} + \cdots + 10\!\cdots\!32 \)
T^7 + 26*T^6 - 236780*T^5 + 5550018*T^4 + 14894851714*T^3 - 1074896050036*T^2 - 132550860710356*T + 10122560081916432
$53$
\( T^{7} + 892 T^{6} + \cdots + 29\!\cdots\!04 \)
T^7 + 892*T^6 - 62800*T^5 - 238392912*T^4 - 46797561808*T^3 + 10458228051520*T^2 + 3876948294875392*T + 299031005866466304
$59$
\( T^{7} + 916 T^{6} + \cdots + 28\!\cdots\!12 \)
T^7 + 916*T^6 - 123208*T^5 - 233985696*T^4 - 47491257408*T^3 - 531465445888*T^2 + 505521966148096*T + 28479386482163712
$61$
\( T^{7} + 450 T^{6} + \cdots + 94\!\cdots\!64 \)
T^7 + 450*T^6 - 235812*T^5 - 183652824*T^4 - 40851480640*T^3 - 3296787753600*T^2 + 10292052238592*T + 9498640387486464
$67$
\( T^{7} + 142 T^{6} + \cdots + 58\!\cdots\!72 \)
T^7 + 142*T^6 - 642332*T^5 + 65653938*T^4 + 112929359326*T^3 - 35666201486416*T^2 + 2884417851730348*T + 5868184351378472
$71$
\( T^{7} - 390 T^{6} + \cdots - 27\!\cdots\!16 \)
T^7 - 390*T^6 - 1391616*T^5 + 443320258*T^4 + 559373970554*T^3 - 111811019797612*T^2 - 62722205428135828*T - 2757114227142688416
$73$
\( T^{7} - 882 T^{6} + \cdots + 32\!\cdots\!68 \)
T^7 - 882*T^6 - 490176*T^5 + 366465940*T^4 + 97669252004*T^3 - 38660731216696*T^2 - 7871564940677120*T + 327134913183527168
$79$
\( T^{7} - 2890 T^{6} + \cdots + 70\!\cdots\!76 \)
T^7 - 2890*T^6 + 2502740*T^5 - 404172954*T^4 - 340489735902*T^3 + 141593598053428*T^2 - 18014507230596692*T + 709712543616204176
$83$
\( T^{7} - 1368 T^{6} + \cdots + 36\!\cdots\!24 \)
T^7 - 1368*T^6 - 868528*T^5 + 1619985024*T^4 - 61918829696*T^3 - 440419564711424*T^2 + 102896348923426816*T + 3618080979671425024
$89$
\( T^{7} + 2006 T^{6} + \cdots - 12\!\cdots\!24 \)
T^7 + 2006*T^6 + 452612*T^5 - 968272360*T^4 - 391846554768*T^3 + 42966566995104*T^2 + 175172262213056*T - 12035202380657024
$97$
\( T^{7} + 1950 T^{6} + \cdots + 14\!\cdots\!04 \)
T^7 + 1950*T^6 - 1232588*T^5 - 2262993896*T^4 + 958171398448*T^3 + 101509360477088*T^2 - 33390013908232256*T + 1490479386278373504
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