[N,k,chi] = [112,10,Mod(1,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, 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("112.1");
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
\(2\)
\(1\)
\(7\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{3} - 92T_{3}^{2} - 51228T_{3} + 379584 \)
T3^3 - 92*T3^2 - 51228*T3 + 379584
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(112))\).
$p$
$F_p(T)$
$2$
\( T^{3} \)
T^3
$3$
\( T^{3} - 92 T^{2} - 51228 T + 379584 \)
T^3 - 92*T^2 - 51228*T + 379584
$5$
\( T^{3} - 274 T^{2} + \cdots - 162790400 \)
T^3 - 274*T^2 - 955840*T - 162790400
$7$
\( (T - 2401)^{3} \)
(T - 2401)^3
$11$
\( T^{3} - 45364 T^{2} + \cdots + 3858186796800 \)
T^3 - 45364*T^2 + 283468672*T + 3858186796800
$13$
\( T^{3} + \cdots + 467510359287776 \)
T^3 + 11158*T^2 - 12383339200*T + 467510359287776
$17$
\( T^{3} + 55866 T^{2} + \cdots + 23\!\cdots\!32 \)
T^3 + 55866*T^2 - 179463473316*T + 23598323295100632
$19$
\( T^{3} + 488772 T^{2} + \cdots - 36\!\cdots\!88 \)
T^3 + 488772*T^2 - 73310959740*T - 36900030983517088
$23$
\( T^{3} - 253888 T^{2} + \cdots + 83\!\cdots\!52 \)
T^3 - 253888*T^2 - 1642558928640*T + 834635574555697152
$29$
\( T^{3} + 765318 T^{2} + \cdots + 28\!\cdots\!24 \)
T^3 + 765318*T^2 - 19696310825508*T + 28859183542903242024
$31$
\( T^{3} - 8189680 T^{2} + \cdots + 35\!\cdots\!40 \)
T^3 - 8189680*T^2 - 8935420033072*T + 35639194223918899840
$37$
\( T^{3} - 7208194 T^{2} + \cdots - 33\!\cdots\!76 \)
T^3 - 7208194*T^2 - 158851332168196*T - 330711692952382326776
$41$
\( T^{3} + 57891986 T^{2} + \cdots - 99\!\cdots\!68 \)
T^3 + 57891986*T^2 + 519485799016124*T - 9954746859096353856968
$43$
\( T^{3} - 37304708 T^{2} + \cdots + 45\!\cdots\!16 \)
T^3 - 37304708*T^2 - 38844634083968*T + 4536811459133903625216
$47$
\( T^{3} - 29210992 T^{2} + \cdots + 24\!\cdots\!16 \)
T^3 - 29210992*T^2 - 929737043478448*T + 24102508490699481798016
$53$
\( T^{3} - 45140082 T^{2} + \cdots + 17\!\cdots\!84 \)
T^3 - 45140082*T^2 - 3695462106447636*T + 170423731840494152591784
$59$
\( T^{3} - 205334804 T^{2} + \cdots - 98\!\cdots\!56 \)
T^3 - 205334804*T^2 + 11479223444283012*T - 98659889651244601457856
$61$
\( T^{3} + 109264870 T^{2} + \cdots - 17\!\cdots\!52 \)
T^3 + 109264870*T^2 - 28481387503181664*T - 1740566215097430705101952
$67$
\( T^{3} - 52322348 T^{2} + \cdots + 82\!\cdots\!92 \)
T^3 - 52322348*T^2 - 37113342345443792*T + 827274306433518943545792
$71$
\( T^{3} - 150048136 T^{2} + \cdots + 54\!\cdots\!36 \)
T^3 - 150048136*T^2 - 42934574873989120*T + 5475179893848238989377536
$73$
\( T^{3} - 761429998 T^{2} + \cdots - 11\!\cdots\!60 \)
T^3 - 761429998*T^2 + 174908424603863468*T - 11208913992148924528155560
$79$
\( T^{3} - 214389152 T^{2} + \cdots + 15\!\cdots\!44 \)
T^3 - 214389152*T^2 - 91090962740890816*T + 15925685359083361526457344
$83$
\( T^{3} - 36110892 T^{2} + \cdots - 27\!\cdots\!16 \)
T^3 - 36110892*T^2 - 61714222303091292*T - 2736987463948980217901216
$89$
\( T^{3} - 1319848398 T^{2} + \cdots + 18\!\cdots\!04 \)
T^3 - 1319848398*T^2 + 167684948573346540*T + 185719562814359872888783704
$97$
\( T^{3} - 101766310 T^{2} + \cdots + 92\!\cdots\!28 \)
T^3 - 101766310*T^2 - 1711607112493817508*T + 922512046108153075458199128
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