[N,k,chi] = [1932,4,Mod(1,1932)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1932, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1932.1");
S:= CuspForms(chi, 4);
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
\(2\)
\(-1\)
\(3\)
\(1\)
\(7\)
\(1\)
\(23\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{9} + 15 T_{5}^{8} - 443 T_{5}^{7} - 6107 T_{5}^{6} + 55861 T_{5}^{5} + 651995 T_{5}^{4} - 2196982 T_{5}^{3} - 15814876 T_{5}^{2} + 33388104 T_{5} + 15217536 \)
T5^9 + 15*T5^8 - 443*T5^7 - 6107*T5^6 + 55861*T5^5 + 651995*T5^4 - 2196982*T5^3 - 15814876*T5^2 + 33388104*T5 + 15217536
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1932))\).
$p$
$F_p(T)$
$2$
\( T^{9} \)
T^9
$3$
\( (T + 3)^{9} \)
(T + 3)^9
$5$
\( T^{9} + 15 T^{8} - 443 T^{7} + \cdots + 15217536 \)
T^9 + 15*T^8 - 443*T^7 - 6107*T^6 + 55861*T^5 + 651995*T^4 - 2196982*T^3 - 15814876*T^2 + 33388104*T + 15217536
$7$
\( (T + 7)^{9} \)
(T + 7)^9
$11$
\( T^{9} - 49 T^{8} + \cdots - 6547555325952 \)
T^9 - 49*T^8 - 5066*T^7 + 177078*T^6 + 10028269*T^5 - 175585445*T^4 - 8197112068*T^3 + 26383346816*T^2 + 1372792633344*T - 6547555325952
$13$
\( T^{9} + 19 T^{8} + \cdots + 5749606538928 \)
T^9 + 19*T^8 - 10991*T^7 + 3227*T^6 + 37295237*T^5 - 570977869*T^4 - 27768049488*T^3 + 417424004312*T^2 + 4303449667632*T + 5749606538928
$17$
\( T^{9} + 12 T^{8} + \cdots + 35\!\cdots\!56 \)
T^9 + 12*T^8 - 32568*T^7 - 719718*T^6 + 360292107*T^5 + 9865208362*T^4 - 1533984709548*T^3 - 40393542972968*T^2 + 2061588010278336*T + 35150831326304256
$19$
\( T^{9} - 63 T^{8} + \cdots + 29\!\cdots\!36 \)
T^9 - 63*T^8 - 47946*T^7 + 1872278*T^6 + 759583457*T^5 - 6352219879*T^4 - 4050569236872*T^3 - 118495301259456*T^2 + 380148482601792*T + 29904251926772736
$23$
\( (T - 23)^{9} \)
(T - 23)^9
$29$
\( T^{9} + 193 T^{8} + \cdots + 40\!\cdots\!28 \)
T^9 + 193*T^8 - 135574*T^7 - 24044646*T^6 + 6040406165*T^5 + 901054679565*T^4 - 109811475817088*T^3 - 11869839514187080*T^2 + 660221867574300912*T + 40331629306759042128
$31$
\( T^{9} + 400 T^{8} + \cdots + 76\!\cdots\!52 \)
T^9 + 400*T^8 - 58338*T^7 - 29693764*T^6 + 1627112741*T^5 + 736337108180*T^4 - 32970220301284*T^3 - 5895660169944016*T^2 + 237029715711103296*T + 7687664485123594752
$37$
\( T^{9} + 253 T^{8} + \cdots + 47\!\cdots\!68 \)
T^9 + 253*T^8 - 181450*T^7 - 38531726*T^6 + 10880004237*T^5 + 1613504530065*T^4 - 265604496646500*T^3 - 17813155292399376*T^2 + 1856368811743510464*T + 47491555716031125168
$41$
\( T^{9} + 710 T^{8} + \cdots - 20\!\cdots\!68 \)
T^9 + 710*T^8 - 300843*T^7 - 291219726*T^6 + 6329667303*T^5 + 38037364298834*T^4 + 4779839157487263*T^3 - 1424812550253765714*T^2 - 349763012408255106204*T - 20115299155787667080568
$43$
\( T^{9} + 161 T^{8} + \cdots - 14\!\cdots\!48 \)
T^9 + 161*T^8 - 354997*T^7 - 82479655*T^6 + 35638976009*T^5 + 11592307923311*T^4 - 361891116279000*T^3 - 417703978947384144*T^2 - 45230160291319344384*T - 1459634070188390658048
$47$
\( T^{9} - 292 T^{8} + \cdots + 81\!\cdots\!12 \)
T^9 - 292*T^8 - 312401*T^7 + 43555392*T^6 + 29259589068*T^5 - 1139997486960*T^4 - 897136942749936*T^3 - 27538666624695232*T^2 + 2180852119693330176*T + 81855320282961856512
$53$
\( T^{9} + 867 T^{8} + \cdots + 11\!\cdots\!12 \)
T^9 + 867*T^8 - 489051*T^7 - 662854269*T^6 - 91878285041*T^5 + 98516196698029*T^4 + 41020914675287250*T^3 + 5069793286838422404*T^2 + 102547619783907505992*T + 115286519885740588512
$59$
\( T^{9} + 259 T^{8} + \cdots + 15\!\cdots\!48 \)
T^9 + 259*T^8 - 1523797*T^7 - 210000791*T^6 + 801790561093*T^5 + 8471528884905*T^4 - 154611667996388634*T^3 + 15037085151003877416*T^2 + 4163410369704745031328*T + 153135806394970765266048
$61$
\( T^{9} + 1105 T^{8} + \cdots + 13\!\cdots\!36 \)
T^9 + 1105*T^8 - 686657*T^7 - 839415987*T^6 + 128938185517*T^5 + 144901520861683*T^4 - 18981033095610504*T^3 - 3491837067310095432*T^2 + 81988977898357216656*T + 13894734215011548220336
$67$
\( T^{9} + 338 T^{8} + \cdots + 17\!\cdots\!12 \)
T^9 + 338*T^8 - 1441551*T^7 - 468260656*T^6 + 539599801679*T^5 + 188520604829712*T^4 - 31953649490472880*T^3 - 11568787821607115776*T^2 + 616168606051532365824*T + 174409536395335694221312
$71$
\( T^{9} - 374 T^{8} + \cdots - 13\!\cdots\!76 \)
T^9 - 374*T^8 - 942347*T^7 + 373623118*T^6 + 199437820237*T^5 - 78982290748338*T^4 - 3015761659526152*T^3 + 2110396738921247360*T^2 - 6884372877222561792*T - 13927746406137430142976
$73$
\( T^{9} - 6 T^{8} + \cdots + 64\!\cdots\!08 \)
T^9 - 6*T^8 - 1296690*T^7 + 365927416*T^6 + 217050483117*T^5 - 75665171966858*T^4 - 1521035201317948*T^3 + 1227544781994604360*T^2 - 41770507619220591264*T + 64442321230866859008
$79$
\( T^{9} - 888 T^{8} + \cdots - 44\!\cdots\!24 \)
T^9 - 888*T^8 - 1963820*T^7 + 1363115586*T^6 + 1354960288723*T^5 - 666680079165426*T^4 - 345639264843313488*T^3 + 112917316343731886464*T^2 + 17387742544884384143360*T - 4499512670194586133069824
$83$
\( T^{9} - 656 T^{8} + \cdots + 76\!\cdots\!16 \)
T^9 - 656*T^8 - 2068132*T^7 + 1048606742*T^6 + 1508533479267*T^5 - 465144562187102*T^4 - 464944824748872616*T^3 + 31524592766367695232*T^2 + 55940979296806110335104*T + 7679818750919022192329216
$89$
\( T^{9} + 858 T^{8} + \cdots + 35\!\cdots\!28 \)
T^9 + 858*T^8 - 2906753*T^7 - 2656896504*T^6 + 1892766231039*T^5 + 1718110688667498*T^4 - 326712039831751416*T^3 - 308022254394890609392*T^2 - 18980955376407902354640*T + 3578118125332344047216928
$97$
\( T^{9} - 757 T^{8} + \cdots - 30\!\cdots\!48 \)
T^9 - 757*T^8 - 4252086*T^7 + 1088233718*T^6 + 6686570676757*T^5 + 1551926778010791*T^4 - 3408569027715418128*T^3 - 2338029203458956056408*T^2 - 510588205913524177056656*T - 30065574631569493355496848
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