[N,k,chi] = [930,2,Mod(481,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.481");
S:= CuspForms(chi, 2);
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
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\)
\(187\)
\(311\)
\(871\)
\(\chi(n)\)
\(1\)
\(1\)
\(\beta_{3}\)
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 subspace can be constructed as the kernel of the linear operator
\( T_{7}^{12} + T_{7}^{11} + 15 T_{7}^{10} - 25 T_{7}^{9} + 306 T_{7}^{8} - 875 T_{7}^{7} + 7459 T_{7}^{6} - 26150 T_{7}^{5} + 106561 T_{7}^{4} - 212490 T_{7}^{3} + 392040 T_{7}^{2} - 303264 T_{7} + 104976 \)
T7^12 + T7^11 + 15*T7^10 - 25*T7^9 + 306*T7^8 - 875*T7^7 + 7459*T7^6 - 26150*T7^5 + 106561*T7^4 - 212490*T7^3 + 392040*T7^2 - 303264*T7 + 104976
acting on \(S_{2}^{\mathrm{new}}(930, [\chi])\).
$p$
$F_p(T)$
$2$
\( (T^{4} - T^{3} + T^{2} - T + 1)^{3} \)
(T^4 - T^3 + T^2 - T + 1)^3
$3$
\( (T^{4} - T^{3} + T^{2} - T + 1)^{3} \)
(T^4 - T^3 + T^2 - T + 1)^3
$5$
\( (T - 1)^{12} \)
(T - 1)^12
$7$
\( T^{12} + T^{11} + 15 T^{10} + \cdots + 104976 \)
T^12 + T^11 + 15*T^10 - 25*T^9 + 306*T^8 - 875*T^7 + 7459*T^6 - 26150*T^5 + 106561*T^4 - 212490*T^3 + 392040*T^2 - 303264*T + 104976
$11$
\( T^{12} - 14 T^{11} + 125 T^{10} + \cdots + 22801 \)
T^12 - 14*T^11 + 125*T^10 - 735*T^9 + 3141*T^8 - 10325*T^7 + 29139*T^6 - 68080*T^5 + 123091*T^4 - 156740*T^3 + 145340*T^2 - 81389*T + 22801
$13$
\( T^{12} - 4 T^{11} + 40 T^{9} + 226 T^{8} + \cdots + 121 \)
T^12 - 4*T^11 + 40*T^9 + 226*T^8 - 170*T^7 + 1029*T^6 - 1100*T^5 + 2101*T^4 - 1970*T^3 + 1215*T^2 + 66*T + 121
$17$
\( T^{12} + 7 T^{11} + 37 T^{10} + \cdots + 64883025 \)
T^12 + 7*T^11 + 37*T^10 + 70*T^9 + 1476*T^8 + 13735*T^7 + 126423*T^6 + 543506*T^5 + 2642386*T^4 + 9367740*T^3 + 30713940*T^2 - 8941050*T + 64883025
$19$
\( T^{12} - 12 T^{11} + 69 T^{10} + \cdots + 4000000 \)
T^12 - 12*T^11 + 69*T^10 - 168*T^9 + 701*T^8 - 2840*T^7 + 22565*T^6 - 88100*T^5 + 338025*T^4 - 771000*T^3 + 2840000*T^2 - 2600000*T + 4000000
$23$
\( T^{12} + 6 T^{11} + 13 T^{10} + \cdots + 93025 \)
T^12 + 6*T^11 + 13*T^10 + 5*T^9 + 1186*T^8 - 775*T^7 + 5872*T^6 + 62927*T^5 + 257576*T^4 - 64805*T^3 + 690115*T^2 + 138775*T + 93025
$29$
\( T^{12} + 23 T^{11} + 264 T^{10} + \cdots + 1229881 \)
T^12 + 23*T^11 + 264*T^10 + 1808*T^9 + 8937*T^8 + 30482*T^7 + 77789*T^6 + 127909*T^5 + 208249*T^4 + 77601*T^3 + 700847*T^2 - 1319710*T + 1229881
$31$
\( T^{12} - 34 T^{11} + \cdots + 887503681 \)
T^12 - 34*T^11 + 492*T^10 - 3523*T^9 + 6018*T^8 + 114442*T^7 - 1072707*T^6 + 3547702*T^5 + 5783298*T^4 - 104953693*T^3 + 454372332*T^2 - 973391134*T + 887503681
$37$
\( (T^{6} - 11 T^{5} - 198 T^{4} + \cdots + 472249)^{2} \)
(T^6 - 11*T^5 - 198*T^4 + 2617*T^3 + 5398*T^2 - 155911*T + 472249)^2
$41$
\( T^{12} - 15 T^{11} + 271 T^{10} + \cdots + 5856400 \)
T^12 - 15*T^11 + 271*T^10 - 2555*T^9 + 24046*T^8 - 176255*T^7 + 1013821*T^6 - 4283450*T^5 + 13106201*T^4 - 26054050*T^3 + 31658440*T^2 - 20231200*T + 5856400
$43$
\( T^{12} + 17 T^{11} + \cdots + 22817915136 \)
T^12 + 17*T^11 + 345*T^10 + 3375*T^9 + 43206*T^8 + 245885*T^7 + 2984451*T^6 - 3537865*T^5 + 138783181*T^4 + 283459740*T^3 + 7924214160*T^2 + 21224576448*T + 22817915136
$47$
\( T^{12} + 2 T^{11} + 134 T^{10} + \cdots + 4405801 \)
T^12 + 2*T^11 + 134*T^10 + 1442*T^9 + 7052*T^8 + 13378*T^7 + 14209*T^6 + 52241*T^5 + 426374*T^4 + 1394554*T^3 + 3559517*T^2 + 4040575*T + 4405801
$53$
\( T^{12} + 21 T^{11} + 407 T^{10} + \cdots + 8294400 \)
T^12 + 21*T^11 + 407*T^10 + 4383*T^9 + 41980*T^8 + 309267*T^7 + 2184467*T^6 + 3015609*T^5 - 3902639*T^4 - 10620600*T^3 + 45109440*T^2 + 10713600*T + 8294400
$59$
\( T^{12} + 15 T^{11} + \cdots + 5935315681 \)
T^12 + 15*T^11 + 108*T^10 + 368*T^9 + 6979*T^8 + 68608*T^7 + 727181*T^6 + 5350541*T^5 + 39907837*T^4 + 197536351*T^3 + 962543721*T^2 + 2305374884*T + 5935315681
$61$
\( (T^{6} - 8 T^{5} - 141 T^{4} + 918 T^{3} + \cdots + 32400)^{2} \)
(T^6 - 8*T^5 - 141*T^4 + 918*T^3 + 3971*T^2 - 29340*T + 32400)^2
$67$
\( (T^{6} - 12 T^{5} - 134 T^{4} + \cdots + 14400)^{2} \)
(T^6 - 12*T^5 - 134*T^4 + 805*T^3 + 8035*T^2 + 19200*T + 14400)^2
$71$
\( T^{12} - 23 T^{11} + 385 T^{10} + \cdots + 8737936 \)
T^12 - 23*T^11 + 385*T^10 - 3495*T^9 + 18336*T^8 - 42545*T^7 + 172091*T^6 - 620655*T^5 + 711331*T^4 + 6312750*T^3 + 32691600*T^2 - 9080832*T + 8737936
$73$
\( T^{12} - 56 T^{11} + \cdots + 9591460096 \)
T^12 - 56*T^11 + 1497*T^10 - 24252*T^9 + 269613*T^8 - 2241132*T^7 + 15220433*T^6 - 86242912*T^5 + 404938953*T^4 - 1486105492*T^3 + 4235125072*T^2 - 6968734016*T + 9591460096
$79$
\( T^{12} + 9 T^{11} + 35 T^{10} + \cdots + 96412761 \)
T^12 + 9*T^11 + 35*T^10 + 105*T^9 + 5266*T^8 + 19935*T^7 + 218924*T^6 + 1744755*T^5 + 11630206*T^4 + 40855785*T^3 + 117164295*T^2 + 92553894*T + 96412761
$83$
\( T^{12} + 24 T^{11} + 427 T^{10} + \cdots + 467856 \)
T^12 + 24*T^11 + 427*T^10 + 6558*T^9 + 93668*T^8 + 750918*T^7 + 4551178*T^6 + 15855578*T^5 + 30855013*T^4 + 13532838*T^3 + 81717372*T^2 + 9976824*T + 467856
$89$
\( T^{12} + 27 T^{11} + \cdots + 725386076416 \)
T^12 + 27*T^11 + 968*T^10 + 18571*T^9 + 366843*T^8 + 5150419*T^7 + 60296672*T^6 + 489894301*T^5 + 2451593933*T^4 + 2161113684*T^3 - 19496860112*T^2 + 13650983488*T + 725386076416
$97$
\( T^{12} - 38 T^{11} + \cdots + 1957531536 \)
T^12 - 38*T^11 + 979*T^10 - 14703*T^9 + 169022*T^8 - 907107*T^7 + 5990179*T^6 + 25022661*T^5 + 349773409*T^4 + 1238338344*T^3 + 2511909072*T^2 - 3842591400*T + 1957531536
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