[N,k,chi] = [5,14,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, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.1");
S:= CuspForms(chi, 14);
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
\(5\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{3} - 142T_{2}^{2} - 11144T_{2} + 901248 \)
T2^3 - 142*T2^2 - 11144*T2 + 901248
acting on \(S_{14}^{\mathrm{new}}(\Gamma_0(5))\).
$p$
$F_p(T)$
$2$
\( T^{3} - 142 T^{2} - 11144 T + 901248 \)
T^3 - 142*T^2 - 11144*T + 901248
$3$
\( T^{3} - 416 T^{2} + \cdots - 1364770944 \)
T^3 - 416*T^2 - 2948016*T - 1364770944
$5$
\( (T - 15625)^{3} \)
(T - 15625)^3
$7$
\( T^{3} - 448292 T^{2} + \cdots + 21\!\cdots\!88 \)
T^3 - 448292*T^2 - 25372193664*T + 21268597977381888
$11$
\( T^{3} + 6604004 T^{2} + \cdots + 88\!\cdots\!32 \)
T^3 + 6604004*T^2 + 13558779730672*T + 8884881428085085632
$13$
\( T^{3} + 33501974 T^{2} + \cdots - 15\!\cdots\!04 \)
T^3 + 33501974*T^2 + 212419069004*T - 1563271783694341784504
$17$
\( T^{3} - 83129542 T^{2} + \cdots + 55\!\cdots\!68 \)
T^3 - 83129542*T^2 - 14209778241929204*T + 55487500862316842283768
$19$
\( T^{3} - 97491100 T^{2} + \cdots - 10\!\cdots\!00 \)
T^3 - 97491100*T^2 - 64102118148043600*T - 1037255652409432406600000
$23$
\( T^{3} - 316255836 T^{2} + \cdots - 13\!\cdots\!64 \)
T^3 - 316255836*T^2 - 811651820076302976*T - 133931292277866194455870464
$29$
\( T^{3} - 2236171850 T^{2} + \cdots + 18\!\cdots\!00 \)
T^3 - 2236171850*T^2 - 7912928658864706100*T + 18108913405817953326976845000
$31$
\( T^{3} - 7482994376 T^{2} + \cdots + 61\!\cdots\!12 \)
T^3 - 7482994376*T^2 - 1820388793297310208*T + 6132444377189056555141158912
$37$
\( T^{3} - 31447174242 T^{2} + \cdots + 46\!\cdots\!28 \)
T^3 - 31447174242*T^2 - 3281607129629443284*T + 4639170238873510422337694935528
$41$
\( T^{3} + 10752884434 T^{2} + \cdots - 82\!\cdots\!48 \)
T^3 + 10752884434*T^2 - 1878252325398766086548*T - 8253822336083889128546423172648
$43$
\( T^{3} - 16930554856 T^{2} + \cdots + 34\!\cdots\!16 \)
T^3 - 16930554856*T^2 - 150522473339731981936*T + 348133205240641604230104841216
$47$
\( T^{3} - 31934201692 T^{2} + \cdots + 18\!\cdots\!08 \)
T^3 - 31934201692*T^2 - 6531732290197220637824*T + 189220257698717224894255669425408
$53$
\( T^{3} + 221149123934 T^{2} + \cdots - 33\!\cdots\!44 \)
T^3 + 221149123934*T^2 - 15594088245534104776916*T - 3309568873947408132481597732773144
$59$
\( T^{3} + 55436423900 T^{2} + \cdots + 18\!\cdots\!00 \)
T^3 + 55436423900*T^2 - 244199198813253186040400*T + 18597352789000427095731687195720000
$61$
\( T^{3} - 496161392746 T^{2} + \cdots + 83\!\cdots\!32 \)
T^3 - 496161392746*T^2 - 168084690998783712859828*T + 83764819606760869989955719283778632
$67$
\( T^{3} - 459297824792 T^{2} + \cdots + 78\!\cdots\!68 \)
T^3 - 459297824792*T^2 + 18034682757450178638096*T + 7818389965468583273428628145735168
$71$
\( T^{3} - 521997878336 T^{2} + \cdots - 40\!\cdots\!28 \)
T^3 - 521997878336*T^2 - 1393240981596313522290368*T - 409966168019034664147234020119036928
$73$
\( T^{3} - 2505025571086 T^{2} + \cdots + 11\!\cdots\!36 \)
T^3 - 2505025571086*T^2 + 869287653090325267846124*T + 118212552449667244478372643764878936
$79$
\( T^{3} - 2990636883200 T^{2} + \cdots + 23\!\cdots\!00 \)
T^3 - 2990636883200*T^2 + 782560703023487892614400*T + 2311380614388570099467421892193280000
$83$
\( T^{3} - 5137135467696 T^{2} + \cdots + 18\!\cdots\!76 \)
T^3 - 5137135467696*T^2 + 5391156736632767654808144*T + 1801370671283079270478985360345986176
$89$
\( T^{3} + 19423025958450 T^{2} + \cdots + 22\!\cdots\!00 \)
T^3 + 19423025958450*T^2 + 119534442454068777421253100*T + 226967774209231184184590659394470215000
$97$
\( T^{3} + 11088325396458 T^{2} + \cdots - 56\!\cdots\!92 \)
T^3 + 11088325396458*T^2 - 45947128061731293102745524*T - 565171605450676166255179927624501022792
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