[N,k,chi] = [76,6,Mod(1,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.1");
S:= CuspForms(chi, 6);
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
\( T_{3}^{4} - 10T_{3}^{3} - 875T_{3}^{2} + 5988T_{3} + 123588 \)
T3^4 - 10*T3^3 - 875*T3^2 + 5988*T3 + 123588
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(76))\).
$p$
$F_p(T)$
$2$
\( T^{4} \)
T^4
$3$
\( T^{4} - 10 T^{3} - 875 T^{2} + \cdots + 123588 \)
T^4 - 10*T^3 - 875*T^2 + 5988*T + 123588
$5$
\( T^{4} + 110 T^{3} + \cdots - 14782624 \)
T^4 + 110*T^3 - 6087*T^2 - 809300*T - 14782624
$7$
\( T^{4} - 30 T^{3} - 22476 T^{2} + \cdots - 57950181 \)
T^4 - 30*T^3 - 22476*T^2 + 2204622*T - 57950181
$11$
\( T^{4} - 706 T^{3} + \cdots + 842790380 \)
T^4 - 706*T^3 + 14469*T^2 + 17856160*T + 842790380
$13$
\( T^{4} - 788 T^{3} + \cdots + 15521087536 \)
T^4 - 788*T^3 - 298941*T^2 + 176779672*T + 15521087536
$17$
\( T^{4} - 240 T^{3} + \cdots + 933010219809 \)
T^4 - 240*T^3 - 4066146*T^2 + 260798832*T + 933010219809
$19$
\( (T + 361)^{4} \)
(T + 361)^4
$23$
\( T^{4} - 5884 T^{3} + \cdots - 69330313326016 \)
T^4 - 5884*T^3 - 4333677*T^2 + 58928167792*T - 69330313326016
$29$
\( T^{4} - 5240 T^{3} + \cdots - 37858523058292 \)
T^4 - 5240*T^3 - 21188385*T^2 + 68597297852*T - 37858523058292
$31$
\( T^{4} + \cdots + 129248370446848 \)
T^4 + 860*T^3 - 23116560*T^2 - 11154181696*T + 129248370446848
$37$
\( T^{4} + 20732 T^{3} + \cdots - 47\!\cdots\!40 \)
T^4 + 20732*T^3 - 49568352*T^2 - 2332526971120*T - 4701007501700240
$41$
\( T^{4} + 10204 T^{3} + \cdots + 11\!\cdots\!40 \)
T^4 + 10204*T^3 - 74685948*T^2 - 507593819200*T + 1168932051626240
$43$
\( T^{4} + 12554 T^{3} + \cdots - 23\!\cdots\!44 \)
T^4 + 12554*T^3 - 108385095*T^2 - 1398101372356*T - 2367148348334144
$47$
\( T^{4} + 4826 T^{3} + \cdots + 18\!\cdots\!36 \)
T^4 + 4826*T^3 - 286986975*T^2 + 842949181576*T + 1826425856030336
$53$
\( T^{4} + 76484 T^{3} + \cdots + 75\!\cdots\!64 \)
T^4 + 76484*T^3 + 1958495643*T^2 + 20504517033688*T + 75211347963000464
$59$
\( T^{4} - 23898 T^{3} + \cdots - 12\!\cdots\!48 \)
T^4 - 23898*T^3 - 1139036835*T^2 + 26521861709340*T - 129409346201894748
$61$
\( T^{4} + 32482 T^{3} + \cdots - 38\!\cdots\!32 \)
T^4 + 32482*T^3 - 1347049563*T^2 - 50337215709824*T - 385211274135945332
$67$
\( T^{4} - 5022 T^{3} + \cdots + 50\!\cdots\!68 \)
T^4 - 5022*T^3 - 4416190023*T^2 - 557781344136*T + 508871346363957168
$71$
\( T^{4} - 121300 T^{3} + \cdots + 40\!\cdots\!04 \)
T^4 - 121300*T^3 + 5020185504*T^2 - 81045731523248*T + 406332945301902704
$73$
\( T^{4} + 104700 T^{3} + \cdots + 10\!\cdots\!09 \)
T^4 + 104700*T^3 - 174343674*T^2 - 149622116529924*T + 1025450251801515009
$79$
\( T^{4} - 117128 T^{3} + \cdots - 34\!\cdots\!64 \)
T^4 - 117128*T^3 + 1970108940*T^2 + 129375307451968*T - 3407677020392545664
$83$
\( T^{4} - 92832 T^{3} + \cdots - 20\!\cdots\!16 \)
T^4 - 92832*T^3 - 2488100004*T^2 + 202856324775840*T - 2078981839792132416
$89$
\( T^{4} - 5988 T^{3} + \cdots + 14\!\cdots\!48 \)
T^4 - 5988*T^3 - 24926212848*T^2 + 117828675020736*T + 140817479130527413248
$97$
\( T^{4} - 22972 T^{3} + \cdots + 12\!\cdots\!72 \)
T^4 - 22972*T^3 - 22191139356*T^2 + 281032633234496*T + 120468488594171644672
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