[N,k,chi] = [912,6,Mod(1,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("912.1");
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
\(2\)
\(1\)
\(3\)
\(1\)
\(19\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{5} - 66T_{5}^{4} - 9127T_{5}^{3} + 388332T_{5}^{2} + 21135676T_{5} - 99608816 \)
T5^5 - 66*T5^4 - 9127*T5^3 + 388332*T5^2 + 21135676*T5 - 99608816
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(912))\).
$p$
$F_p(T)$
$2$
\( T^{5} \)
T^5
$3$
\( (T + 9)^{5} \)
(T + 9)^5
$5$
\( T^{5} - 66 T^{4} - 9127 T^{3} + \cdots - 99608816 \)
T^5 - 66*T^4 - 9127*T^3 + 388332*T^2 + 21135676*T - 99608816
$7$
\( T^{5} - 2 T^{4} + \cdots + 28578898944 \)
T^5 - 2*T^4 - 53267*T^3 - 536092*T^2 + 609186432*T + 28578898944
$11$
\( T^{5} - 322 T^{4} + \cdots - 5635869502464 \)
T^5 - 322*T^4 - 390239*T^3 + 142100884*T^2 + 14739957888*T - 5635869502464
$13$
\( T^{5} - 1116 T^{4} + \cdots - 13044480271936 \)
T^5 - 1116*T^4 - 256808*T^3 + 371126528*T^2 - 27623928688*T - 13044480271936
$17$
\( T^{5} - 2300 T^{4} + \cdots + 451692086632 \)
T^5 - 2300*T^4 + 1583525*T^3 - 341640186*T^2 + 8451194492*T + 451692086632
$19$
\( (T - 361)^{5} \)
(T - 361)^5
$23$
\( T^{5} + 866 T^{4} + \cdots + 67\!\cdots\!44 \)
T^5 + 866*T^4 - 8856280*T^3 - 5768087968*T^2 + 9944841693312*T + 6768088269318144
$29$
\( T^{5} - 5998 T^{4} + \cdots - 14\!\cdots\!96 \)
T^5 - 5998*T^4 - 32523720*T^3 + 113464970288*T^2 + 323369597354512*T - 142366003291721696
$31$
\( T^{5} + 4126 T^{4} + \cdots - 43\!\cdots\!00 \)
T^5 + 4126*T^4 - 46613420*T^3 - 343216476024*T^2 - 726601242180960*T - 430778889607449600
$37$
\( T^{5} - 5188 T^{4} + \cdots + 21\!\cdots\!16 \)
T^5 - 5188*T^4 - 188209796*T^3 + 320817635408*T^2 + 9666820695936640*T + 21700956369823394816
$41$
\( T^{5} - 27094 T^{4} + \cdots + 48\!\cdots\!24 \)
T^5 - 27094*T^4 + 170358508*T^3 - 323903076584*T^2 - 73999458963264*T + 485689899247041024
$43$
\( T^{5} + 17766 T^{4} + \cdots - 41\!\cdots\!28 \)
T^5 + 17766*T^4 - 47723403*T^3 - 1832256867132*T^2 - 6186638620251920*T - 4153265010714244928
$47$
\( T^{5} + 33436 T^{4} + \cdots - 51\!\cdots\!88 \)
T^5 + 33436*T^4 + 79178205*T^3 - 3412064625970*T^2 - 13341738087492984*T - 5197687406418607488
$53$
\( T^{5} - 14722 T^{4} + \cdots - 59\!\cdots\!64 \)
T^5 - 14722*T^4 - 783989016*T^3 + 8416627390576*T^2 + 57801358639213392*T - 593011462996233410464
$59$
\( T^{5} + 15480 T^{4} + \cdots + 37\!\cdots\!28 \)
T^5 + 15480*T^4 - 1565949776*T^3 - 17591344239296*T^2 + 533634578506904576*T + 3716355548680797795328
$61$
\( T^{5} + 880 T^{4} + \cdots - 13\!\cdots\!56 \)
T^5 + 880*T^4 - 485516199*T^3 + 5060390384254*T^2 - 12427473597188228*T - 13246884062728460056
$67$
\( T^{5} + 4764 T^{4} + \cdots - 96\!\cdots\!56 \)
T^5 + 4764*T^4 - 3916892320*T^3 - 8215357051456*T^2 + 2563829932526526720*T - 9632548661431143315456
$71$
\( T^{5} + 48924 T^{4} + \cdots + 66\!\cdots\!72 \)
T^5 + 48924*T^4 - 4808114896*T^3 - 159239052667648*T^2 + 6265430814040129536*T + 66933527456218110492672
$73$
\( T^{5} - 60196 T^{4} + \cdots + 30\!\cdots\!28 \)
T^5 - 60196*T^4 + 1204920785*T^3 - 7567704160786*T^2 - 24781290633267348*T + 304111795026538961928
$79$
\( T^{5} + 166986 T^{4} + \cdots + 24\!\cdots\!00 \)
T^5 + 166986*T^4 + 4564902832*T^3 - 348910820451200*T^2 - 9446903070343753600*T + 243632774529383145088000
$83$
\( T^{5} + 106352 T^{4} + \cdots - 11\!\cdots\!48 \)
T^5 + 106352*T^4 + 969261264*T^3 - 151402009459584*T^2 - 3619457855839850496*T - 11957588978363484110848
$89$
\( T^{5} + 11466 T^{4} + \cdots + 27\!\cdots\!56 \)
T^5 + 11466*T^4 - 18001754824*T^3 + 55099927285040*T^2 + 32876807120069541648*T + 273408887338763203421856
$97$
\( T^{5} - 183042 T^{4} + \cdots + 10\!\cdots\!24 \)
T^5 - 183042*T^4 + 2729454376*T^3 + 359420830687024*T^2 - 12520187361550521520*T + 105356724308905676432224
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