[N,k,chi] = [5,16,Mod(1,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.1");
S:= CuspForms(chi, 16);
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
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{3} - 4T_{2}^{2} - 59336T_{2} - 5408256 \)
T2^3 - 4*T2^2 - 59336*T2 - 5408256
acting on \(S_{16}^{\mathrm{new}}(\Gamma_0(5))\).
$p$
$F_p(T)$
$2$
\( T^{3} - 4 T^{2} - 59336 T - 5408256 \)
T^3 - 4*T^2 - 59336*T - 5408256
$3$
\( T^{3} - 3518 T^{2} + \cdots + 152116768152 \)
T^3 - 3518*T^2 - 39290964*T + 152116768152
$5$
\( (T + 78125)^{3} \)
(T + 78125)^3
$7$
\( T^{3} + 905206 T^{2} + \cdots - 24\!\cdots\!16 \)
T^3 + 905206*T^2 - 15513501219636*T - 24799626124315625016
$11$
\( T^{3} - 122875456 T^{2} + \cdots + 92\!\cdots\!92 \)
T^3 - 122875456*T^2 + 2060789452429312*T + 92191364086201461768192
$13$
\( T^{3} + 90911522 T^{2} + \cdots - 95\!\cdots\!08 \)
T^3 + 90911522*T^2 - 87066778944810964*T - 9540587864978725737996008
$17$
\( T^{3} + 3868973426 T^{2} + \cdots + 65\!\cdots\!64 \)
T^3 + 3868973426*T^2 + 3356463740530531564*T + 659480640514355036076939864
$19$
\( T^{3} - 3670884220 T^{2} + \cdots + 46\!\cdots\!00 \)
T^3 - 3670884220*T^2 - 19805713993191614800*T + 46556578977074743624211320000
$23$
\( T^{3} - 26698058238 T^{2} + \cdots - 27\!\cdots\!68 \)
T^3 - 26698058238*T^2 + 160793876983625022636*T - 278419468493424326880498744168
$29$
\( T^{3} - 145544932730 T^{2} + \cdots + 75\!\cdots\!00 \)
T^3 - 145544932730*T^2 - 5164594941821459789300*T + 7551508497416041023786941205000
$31$
\( T^{3} + 25873382644 T^{2} + \cdots - 90\!\cdots\!08 \)
T^3 + 25873382644*T^2 - 16569397947960261083088*T - 90170674943252113290885330489408
$37$
\( T^{3} - 419480249934 T^{2} + \cdots + 70\!\cdots\!24 \)
T^3 - 419480249934*T^2 + 2452290868299091165164*T + 7090445062772162615554529314235224
$41$
\( T^{3} - 274005770306 T^{2} + \cdots - 22\!\cdots\!08 \)
T^3 - 274005770306*T^2 - 851514240209783837448788*T - 228907166426580833264301349187021208
$43$
\( T^{3} - 2350065869158 T^{2} + \cdots + 82\!\cdots\!12 \)
T^3 - 2350065869158*T^2 - 714909277065020599989364*T + 828486552490674567603665360650235512
$47$
\( T^{3} + 8891070209486 T^{2} + \cdots - 20\!\cdots\!96 \)
T^3 + 8891070209486*T^2 + 14709242331204977729347564*T - 20986016010832976484489024460745470296
$53$
\( T^{3} - 8749242811318 T^{2} + \cdots + 14\!\cdots\!52 \)
T^3 - 8749242811318*T^2 + 13878270140876493656089036*T + 14269288547715598085048303563324439352
$59$
\( T^{3} + 14173516437140 T^{2} + \cdots + 44\!\cdots\!00 \)
T^3 + 14173516437140*T^2 - 689606782688692758803925200*T + 4491260913844418441633084199257874840000
$61$
\( T^{3} + 38066837721794 T^{2} + \cdots - 18\!\cdots\!08 \)
T^3 + 38066837721794*T^2 + 211075547736993861690192812*T - 1898598056474028596347776578545715272808
$67$
\( T^{3} - 144391638065474 T^{2} + \cdots - 97\!\cdots\!36 \)
T^3 - 144391638065474*T^2 + 6659417768652288868486683564*T - 97724827083859359935000234542095804131736
$71$
\( T^{3} + 126512337318844 T^{2} + \cdots + 13\!\cdots\!92 \)
T^3 + 126512337318844*T^2 + 3181074543640941044369832112*T + 13692330471948005290816353478401658435392
$73$
\( T^{3} - 199804772078038 T^{2} + \cdots + 74\!\cdots\!32 \)
T^3 - 199804772078038*T^2 - 533449685152794806344701364*T + 747658520021748569183740852262182546703032
$79$
\( T^{3} + 73797562093720 T^{2} + \cdots - 65\!\cdots\!00 \)
T^3 + 73797562093720*T^2 - 9773945571393681645250516800*T - 654645305298089329705991709734103357120000
$83$
\( T^{3} + 219109046205402 T^{2} + \cdots + 10\!\cdots\!72 \)
T^3 + 219109046205402*T^2 + 10744839649532345374069597836*T + 106591665794617846747793378994684357034872
$89$
\( T^{3} + 360765737744610 T^{2} + \cdots - 25\!\cdots\!00 \)
T^3 + 360765737744610*T^2 - 145694048087867645090603135700*T - 25008448122936386679086101616495009992065000
$97$
\( T^{3} + 509209931654586 T^{2} + \cdots - 21\!\cdots\!96 \)
T^3 + 509209931654586*T^2 - 105163785644821770445861832436*T - 21317422192367483546390673744946039966533896
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