[N,k,chi] = [603,4,Mod(1,603)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(603, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("603.1");
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
\(3\)
\(-1\)
\(67\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{7} - T_{2}^{6} - 38T_{2}^{5} + 18T_{2}^{4} + 373T_{2}^{3} - 151T_{2}^{2} - 956T_{2} + 498 \)
T2^7 - T2^6 - 38*T2^5 + 18*T2^4 + 373*T2^3 - 151*T2^2 - 956*T2 + 498
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(603))\).
$p$
$F_p(T)$
$2$
\( T^{7} - T^{6} - 38 T^{5} + 18 T^{4} + \cdots + 498 \)
T^7 - T^6 - 38*T^5 + 18*T^4 + 373*T^3 - 151*T^2 - 956*T + 498
$3$
\( T^{7} \)
T^7
$5$
\( T^{7} + 11 T^{6} - 311 T^{5} + \cdots - 1054848 \)
T^7 + 11*T^6 - 311*T^5 - 3339*T^4 + 18232*T^3 + 152084*T^2 - 402656*T - 1054848
$7$
\( T^{7} + 33 T^{6} - 813 T^{5} + \cdots - 3147392 \)
T^7 + 33*T^6 - 813*T^5 - 25653*T^4 + 157960*T^3 + 4069796*T^2 + 12106144*T - 3147392
$11$
\( T^{7} - 130 T^{6} + \cdots - 3855752448 \)
T^7 - 130*T^6 + 3332*T^5 + 242204*T^4 - 16366864*T^3 + 341889872*T^2 - 2204800640*T - 3855752448
$13$
\( T^{7} - 16 T^{6} + \cdots + 36060533248 \)
T^7 - 16*T^6 - 7420*T^5 + 101804*T^4 + 11861664*T^3 - 83011360*T^2 - 4320764672*T + 36060533248
$17$
\( T^{7} + 90 T^{6} + \cdots - 47177769168 \)
T^7 + 90*T^6 - 11647*T^5 - 741348*T^4 + 4573936*T^3 + 510644988*T^2 - 439806336*T - 47177769168
$19$
\( T^{7} + 132 T^{6} + \cdots + 2352293777728 \)
T^7 + 132*T^6 - 20847*T^5 - 2756130*T^4 + 33409996*T^3 + 10344150524*T^2 + 303262093792*T + 2352293777728
$23$
\( T^{7} - 399 T^{6} + \cdots - 176992942356 \)
T^7 - 399*T^6 + 35760*T^5 + 2129442*T^4 - 227335349*T^3 - 6841681467*T^2 - 61349671680*T - 176992942356
$29$
\( T^{7} + \cdots + 154337966321664 \)
T^7 - 302*T^6 - 52031*T^5 + 19669032*T^4 - 12129656*T^3 - 201132112064*T^2 - 1258762021376*T + 154337966321664
$31$
\( T^{7} + 555 T^{6} + \cdots + 6536744991936 \)
T^7 + 555*T^6 + 62859*T^5 - 10676603*T^4 - 2489779584*T^3 - 156415000500*T^2 - 2991759351840*T + 6536744991936
$37$
\( T^{7} - 297 T^{6} + \cdots + 18\!\cdots\!52 \)
T^7 - 297*T^6 - 110314*T^5 + 37180714*T^4 + 1391707057*T^3 - 860056536469*T^2 + 15483762194784*T + 1869377879267452
$41$
\( T^{7} - 717 T^{6} + \cdots - 17\!\cdots\!28 \)
T^7 - 717*T^6 + 42351*T^5 + 79095387*T^4 - 21479445008*T^3 + 1129112790156*T^2 + 183931387391136*T - 17242449775763328
$43$
\( T^{7} + 245 T^{6} + \cdots + 15\!\cdots\!28 \)
T^7 + 245*T^6 - 196853*T^5 - 40486813*T^4 + 7908867920*T^3 + 754637680300*T^2 - 90851114080864*T + 1548639507886528
$47$
\( T^{7} - 1072 T^{6} + \cdots + 50\!\cdots\!08 \)
T^7 - 1072*T^6 - 25619*T^5 + 306466218*T^4 - 41754150608*T^3 - 25629694307692*T^2 + 3429135102811360*T + 509329567663817808
$53$
\( T^{7} + 265 T^{6} + \cdots - 42\!\cdots\!76 \)
T^7 + 265*T^6 - 286505*T^5 - 54543135*T^4 + 14351577264*T^3 + 1233748587672*T^2 - 178255592312688*T - 4266676954278576
$59$
\( T^{7} - 255 T^{6} + \cdots - 18\!\cdots\!88 \)
T^7 - 255*T^6 - 467682*T^5 + 108879660*T^4 + 41116434381*T^3 - 5214914610417*T^2 - 821323770339096*T - 18641555868243888
$61$
\( T^{7} - 418 T^{6} + \cdots + 34\!\cdots\!16 \)
T^7 - 418*T^6 - 1055320*T^5 + 499348852*T^4 + 281576945280*T^3 - 151908828671088*T^2 - 1217851354362240*T + 3469198900886822016
$67$
\( (T - 67)^{7} \)
(T - 67)^7
$71$
\( T^{7} - 1194 T^{6} + \cdots + 10\!\cdots\!92 \)
T^7 - 1194*T^6 - 385648*T^5 + 533522196*T^4 + 30269837920*T^3 - 60583974841200*T^2 + 99345100376064*T + 1076891416180641792
$73$
\( T^{7} - 995 T^{6} + \cdots + 22\!\cdots\!52 \)
T^7 - 995*T^6 - 727554*T^5 + 917239802*T^4 - 80442081391*T^3 - 67315378611963*T^2 - 2966909849263184*T + 223586300350585252
$79$
\( T^{7} + 2640 T^{6} + \cdots + 18\!\cdots\!84 \)
T^7 + 2640*T^6 + 695940*T^5 - 3457694208*T^4 - 3070309349216*T^3 + 4714300780352*T^2 + 750188029356388864*T + 187709359109641590784
$83$
\( T^{7} - 2579 T^{6} + \cdots - 50\!\cdots\!32 \)
T^7 - 2579*T^6 + 1792391*T^5 + 338971921*T^4 - 774034371304*T^3 + 239921363400592*T^2 - 18433623167376128*T - 501776391052741632
$89$
\( T^{7} - 1604 T^{6} + \cdots + 19\!\cdots\!92 \)
T^7 - 1604*T^6 - 1366939*T^5 + 2875293478*T^4 - 25819905184*T^3 - 1148930826815996*T^2 + 270796837715500480*T + 19968552128646898992
$97$
\( T^{7} + 808 T^{6} + \cdots - 88\!\cdots\!16 \)
T^7 + 808*T^6 - 3474348*T^5 - 1589996796*T^4 + 3725187429456*T^3 + 445248769886352*T^2 - 803499897194392320*T - 88371724628719132416
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