[N,k,chi] = [115,6,Mod(1,115)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(115, 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("115.1");
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
\(5\)
\(1\)
\(23\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{7} - 4T_{2}^{6} - 193T_{2}^{5} + 526T_{2}^{4} + 10874T_{2}^{3} - 12768T_{2}^{2} - 150624T_{2} - 91152 \)
T2^7 - 4*T2^6 - 193*T2^5 + 526*T2^4 + 10874*T2^3 - 12768*T2^2 - 150624*T2 - 91152
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(115))\).
$p$
$F_p(T)$
$2$
\( T^{7} - 4 T^{6} - 193 T^{5} + \cdots - 91152 \)
T^7 - 4*T^6 - 193*T^5 + 526*T^4 + 10874*T^3 - 12768*T^2 - 150624*T - 91152
$3$
\( T^{7} + 3 T^{6} - 1066 T^{5} + \cdots - 71539200 \)
T^7 + 3*T^6 - 1066*T^5 + 1371*T^4 + 264735*T^3 + 169020*T^2 - 19984320*T - 71539200
$5$
\( (T + 25)^{7} \)
(T + 25)^7
$7$
\( T^{7} - 33 T^{6} + \cdots + 11741977345536 \)
T^7 - 33*T^6 - 31476*T^5 + 2640617*T^4 + 94916373*T^3 - 12531933542*T^2 + 31882608380*T + 11741977345536
$11$
\( T^{7} - 1373 T^{6} + \cdots - 12\!\cdots\!96 \)
T^7 - 1373*T^6 + 361243*T^5 + 155765878*T^4 - 57718679088*T^3 - 887834468216*T^2 + 1627298495226352*T - 120544914304596096
$13$
\( T^{7} - 605 T^{6} + \cdots - 25\!\cdots\!28 \)
T^7 - 605*T^6 - 1317308*T^5 + 992298595*T^4 + 131663797643*T^3 - 120683268331630*T^2 - 19682239033686684*T - 253392679999951128
$17$
\( T^{7} - 2505 T^{6} + \cdots - 25\!\cdots\!20 \)
T^7 - 2505*T^6 - 992146*T^5 + 6631007277*T^4 - 5763009183913*T^3 + 1840350568120298*T^2 - 186529321434538248*T - 2587841391685165920
$19$
\( T^{7} + 115 T^{6} + \cdots + 53\!\cdots\!40 \)
T^7 + 115*T^6 - 11465015*T^5 - 3404339738*T^4 + 30330123541272*T^3 + 2391328437183016*T^2 - 16994751977463107984*T + 537735195650421690240
$23$
\( (T - 529)^{7} \)
(T - 529)^7
$29$
\( T^{7} - 2440 T^{6} + \cdots + 11\!\cdots\!00 \)
T^7 - 2440*T^6 - 44305286*T^5 + 47895567500*T^4 + 307372139493069*T^3 - 331501125214383116*T^2 + 55555629420892972248*T + 11921748756012815567400
$31$
\( T^{7} - 13565 T^{6} + \cdots - 11\!\cdots\!20 \)
T^7 - 13565*T^6 + 32695491*T^5 + 213107112724*T^4 - 808114409531027*T^3 - 639508426865702615*T^2 + 3316676507819987010775*T - 1102707579132703587273720
$37$
\( T^{7} - 9414 T^{6} + \cdots - 23\!\cdots\!56 \)
T^7 - 9414*T^6 - 84006975*T^5 + 501716023384*T^4 + 3079975977535176*T^3 - 2825366625060352600*T^2 - 25872894272345683780288*T - 23057017847618399883689856
$41$
\( T^{7} - 13725 T^{6} + \cdots + 67\!\cdots\!90 \)
T^7 - 13725*T^6 - 283001365*T^5 + 3891154770912*T^4 + 20554897455883859*T^3 - 296052256919795724485*T^2 - 450082710393325037894367*T + 6755087762816836930550886690
$43$
\( T^{7} - 76694 T^{6} + \cdots + 30\!\cdots\!00 \)
T^7 - 76694*T^6 + 2239976732*T^5 - 29408715072944*T^4 + 121468334762689984*T^3 + 970538575882729175040*T^2 - 11254650982635779865395200*T + 30785876292714497547108352000
$47$
\( T^{7} - 59692 T^{6} + \cdots + 14\!\cdots\!40 \)
T^7 - 59692*T^6 + 1016719717*T^5 + 3223646057946*T^4 - 270442297607619492*T^3 + 2897660743909917813920*T^2 - 11782452353645957289016320*T + 14293773020095115982129930240
$53$
\( T^{7} - 49536 T^{6} + \cdots + 14\!\cdots\!12 \)
T^7 - 49536*T^6 + 406734397*T^5 + 11346263588694*T^4 - 145060452165645528*T^3 - 740594139969679345712*T^2 + 10127494515325475342664528*T + 14322187770661539153697334112
$59$
\( T^{7} - 44536 T^{6} + \cdots - 13\!\cdots\!88 \)
T^7 - 44536*T^6 + 526605337*T^5 + 1364735664118*T^4 - 54494394751112380*T^3 + 241848523899960871536*T^2 + 58523194505512156607424*T - 1305528836914493280902469888
$61$
\( T^{7} + 49097 T^{6} + \cdots - 17\!\cdots\!52 \)
T^7 + 49097*T^6 - 1258515243*T^5 - 89108916433808*T^4 - 193453259880044536*T^3 + 40377339369769081142456*T^2 + 456818839573049625464884992*T - 178378214416320934714306161152
$67$
\( T^{7} - 788 T^{6} + \cdots + 20\!\cdots\!80 \)
T^7 - 788*T^6 - 4364515503*T^5 + 20017811939038*T^4 + 1985695016034029284*T^3 - 2686431148202932595920*T^2 - 117597110099649812140199360*T + 205138350647722274742012692480
$71$
\( T^{7} - 49521 T^{6} + \cdots - 27\!\cdots\!00 \)
T^7 - 49521*T^6 - 4152557019*T^5 + 132289876826572*T^4 + 4564542611095818045*T^3 - 51025537950833072697115*T^2 - 1211357768552696721059395915*T - 2789532065331321458815739362200
$73$
\( T^{7} + 3760 T^{6} + \cdots + 72\!\cdots\!16 \)
T^7 + 3760*T^6 - 8604461013*T^5 + 38861320663420*T^4 + 20211085170535855244*T^3 - 214985342996682736936792*T^2 - 7615453247861595669158576288*T + 72823403132849627943035449888416
$79$
\( T^{7} - 918 T^{6} + \cdots + 14\!\cdots\!64 \)
T^7 - 918*T^6 - 8655220124*T^5 + 200092800448736*T^4 + 17794847635956051520*T^3 - 781661033190353111634432*T^2 + 7871005038811947498556682240*T + 14775794279830965217981257252864
$83$
\( T^{7} - 99202 T^{6} + \cdots - 77\!\cdots\!88 \)
T^7 - 99202*T^6 - 640074395*T^5 + 358033066765736*T^4 - 10635790343136533340*T^3 - 96374075025489181757232*T^2 + 7607195737217480736869345600*T - 77956803520279055469240239781888
$89$
\( T^{7} + 141676 T^{6} + \cdots - 16\!\cdots\!20 \)
T^7 + 141676*T^6 - 19502968664*T^5 - 3030755959851160*T^4 + 78543845802648032224*T^3 + 16353744067796559281909248*T^2 + 36744016840776454480542944768*T - 16739394980258882213157037648926720
$97$
\( T^{7} - 28731 T^{6} + \cdots - 11\!\cdots\!16 \)
T^7 - 28731*T^6 - 18827632711*T^5 + 107445861776488*T^4 + 94163997189991482044*T^3 + 1506519993624751698558200*T^2 - 61686983984959435855431765248*T - 1198115790778562451957356160573216
show more
show less