[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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\)
\(187\)
\(311\)
\(871\)
\(\chi(n)\)
\(1\)
\(1\)
\(-\beta_{6}\)
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
\( T_{7}^{16} + 7 T_{7}^{15} + 49 T_{7}^{14} + 176 T_{7}^{13} + 714 T_{7}^{12} + 1445 T_{7}^{11} + 5737 T_{7}^{10} - 3063 T_{7}^{9} + 16548 T_{7}^{8} - 28408 T_{7}^{7} + 73817 T_{7}^{6} + 6515 T_{7}^{5} + 24239 T_{7}^{4} + \cdots + 16 \)
T7^16 + 7*T7^15 + 49*T7^14 + 176*T7^13 + 714*T7^12 + 1445*T7^11 + 5737*T7^10 - 3063*T7^9 + 16548*T7^8 - 28408*T7^7 + 73817*T7^6 + 6515*T7^5 + 24239*T7^4 - 4074*T7^3 - 56*T7^2 + 112*T7 + 16
acting on \(S_{2}^{\mathrm{new}}(930, [\chi])\).
$p$
$F_p(T)$
$2$
\( (T^{4} - T^{3} + T^{2} - T + 1)^{4} \)
(T^4 - T^3 + T^2 - T + 1)^4
$3$
\( (T^{4} + T^{3} + T^{2} + T + 1)^{4} \)
(T^4 + T^3 + T^2 + T + 1)^4
$5$
\( (T + 1)^{16} \)
(T + 1)^16
$7$
\( T^{16} + 7 T^{15} + 49 T^{14} + 176 T^{13} + \cdots + 16 \)
T^16 + 7*T^15 + 49*T^14 + 176*T^13 + 714*T^12 + 1445*T^11 + 5737*T^10 - 3063*T^9 + 16548*T^8 - 28408*T^7 + 73817*T^6 + 6515*T^5 + 24239*T^4 - 4074*T^3 - 56*T^2 + 112*T + 16
$11$
\( T^{16} - 4 T^{15} + 41 T^{14} + \cdots + 2624400 \)
T^16 - 4*T^15 + 41*T^14 - 219*T^13 + 1611*T^12 - 5605*T^11 + 44145*T^10 - 262190*T^9 + 1927015*T^8 - 7337230*T^7 + 16978940*T^6 - 6832375*T^5 + 17308675*T^4 + 24149250*T^3 + 21222000*T^2 + 8748000*T + 2624400
$13$
\( T^{16} - 2 T^{15} + 20 T^{14} + \cdots + 1256641 \)
T^16 - 2*T^15 + 20*T^14 - 45*T^13 + 995*T^12 - 6226*T^11 + 46187*T^10 - 184380*T^9 + 971955*T^8 - 3121605*T^7 + 8242642*T^6 - 18830749*T^5 + 39554180*T^4 - 43483105*T^3 + 21649855*T^2 + 1229737*T + 1256641
$17$
\( T^{16} - 5 T^{15} + \cdots + 97846342416 \)
T^16 - 5*T^15 + 51*T^14 - 308*T^13 + 3594*T^12 - 1561*T^11 + 118641*T^10 - 235492*T^9 + 3660776*T^8 - 2361738*T^7 + 115502484*T^6 + 92753798*T^5 + 1930076341*T^4 + 4803275082*T^3 + 15459159744*T^2 + 19657854576*T + 97846342416
$19$
\( T^{16} + 2 T^{15} + 19 T^{14} + \cdots + 331776 \)
T^16 + 2*T^15 + 19*T^14 - 9*T^13 + 1784*T^12 + 15305*T^11 + 122042*T^10 + 390467*T^9 + 2186988*T^8 + 6359687*T^7 + 11298737*T^6 + 5386455*T^5 + 21231289*T^4 + 1977096*T^3 + 7375104*T^2 - 2515968*T + 331776
$23$
\( T^{16} + 4 T^{15} + \cdots + 1881824400 \)
T^16 + 4*T^15 + T^14 - 91*T^13 + 4746*T^12 + 35515*T^11 + 319350*T^10 + 774285*T^9 + 6166210*T^8 + 12865555*T^7 + 148665665*T^6 - 590379825*T^5 + 4210608775*T^4 + 3636814350*T^3 + 7123347900*T^2 + 2687391000*T + 1881824400
$29$
\( T^{16} - 5 T^{15} + 26 T^{14} + \cdots + 104976 \)
T^16 - 5*T^15 + 26*T^14 - 472*T^13 + 8569*T^12 - 44644*T^11 + 676831*T^10 - 7376403*T^9 + 53481071*T^8 - 195839417*T^7 + 573318019*T^6 - 27416788*T^5 + 79994221*T^4 - 19202382*T^3 + 3300264*T^2 - 279936*T + 104976
$31$
\( T^{16} + T^{15} + \cdots + 852891037441 \)
T^16 + T^15 - 55*T^14 - 50*T^13 + 1620*T^12 + 5123*T^11 - 49792*T^10 - 127490*T^9 + 1742455*T^8 - 3952190*T^7 - 47850112*T^6 + 152619293*T^5 + 1496104020*T^4 - 1431457550*T^3 - 48812702455*T^2 + 27512614111*T + 852891037441
$37$
\( (T^{8} + 10 T^{7} - 118 T^{6} + \cdots - 223421)^{2} \)
(T^8 + 10*T^7 - 118*T^6 - 1322*T^5 + 325*T^4 + 26438*T^3 + 32060*T^2 - 137404*T - 223421)^2
$41$
\( T^{16} + 17 T^{15} + \cdots + 3088876550400 \)
T^16 + 17*T^15 + 261*T^14 + 3345*T^13 + 40220*T^12 + 305327*T^11 + 2504949*T^10 + 15672912*T^9 + 85663685*T^8 + 251595910*T^7 + 1369899176*T^6 + 3243619432*T^5 + 33154340176*T^4 + 91658991840*T^3 + 326938602240*T^2 + 918901756800*T + 3088876550400
$43$
\( T^{16} + 4 T^{15} + \cdots + 210996910336 \)
T^16 + 4*T^15 - 20*T^14 - 620*T^13 + 11800*T^12 + 59082*T^11 + 951503*T^10 - 6488735*T^9 + 8556840*T^8 + 183954050*T^7 + 3006014983*T^6 - 11053139193*T^5 + 64478771405*T^4 - 119025473820*T^3 + 273098326800*T^2 - 204483412416*T + 210996910336
$47$
\( T^{16} - 2 T^{15} + \cdots + 153836528400 \)
T^16 - 2*T^15 + 74*T^14 + 462*T^13 + 5466*T^12 - 4030*T^11 + 694625*T^10 + 5067865*T^9 + 46773750*T^8 + 55978380*T^7 + 64782035*T^6 - 1992767275*T^5 + 26190010225*T^4 - 29318354400*T^3 + 123746788800*T^2 + 25545288600*T + 153836528400
$53$
\( T^{16} - 9 T^{15} + \cdots + 17398665216 \)
T^16 - 9*T^15 + 15*T^14 - 5*T^13 + 21870*T^12 - 363117*T^11 + 4263423*T^10 - 32683995*T^9 + 225665715*T^8 - 1142577610*T^7 + 6203264688*T^6 - 15476050752*T^5 + 71300346640*T^4 - 91483303680*T^3 + 362981905920*T^2 - 126988729344*T + 17398665216
$59$
\( T^{16} + 3 T^{15} + \cdots + 42855614816400 \)
T^16 + 3*T^15 + 14*T^14 - 88*T^13 + 23131*T^12 - 222290*T^11 + 2633545*T^10 - 10237955*T^9 + 104202115*T^8 - 303381045*T^7 + 4504740435*T^6 - 8967697650*T^5 + 178408244925*T^4 - 157422410550*T^3 + 5745582517500*T^2 + 6007846026600*T + 42855614816400
$61$
\( (T^{8} - 35 T^{7} + 330 T^{6} + \cdots + 356400)^{2} \)
(T^8 - 35*T^7 + 330*T^6 + 1405*T^5 - 40090*T^4 + 206925*T^3 - 222255*T^2 - 467100*T + 356400)^2
$67$
\( (T^{8} + 33 T^{7} + 195 T^{6} + \cdots + 29553984)^{2} \)
(T^8 + 33*T^7 + 195*T^6 - 4449*T^5 - 64070*T^4 - 114846*T^3 + 2470977*T^2 + 16069320*T + 29553984)^2
$71$
\( T^{16} + 25 T^{15} + \cdots + 23444964000000 \)
T^16 + 25*T^15 + 555*T^14 + 9685*T^13 + 158800*T^12 + 1769435*T^11 + 19898885*T^10 + 163642725*T^9 + 1251186375*T^8 + 5329877450*T^7 + 22681953400*T^6 - 17788230200*T^5 + 1491666840400*T^4 + 6929191644000*T^3 + 18109625040000*T^2 + 25382732400000*T + 23444964000000
$73$
\( T^{16} + 10 T^{15} + \cdots + 233420394496 \)
T^16 + 10*T^15 + 259*T^14 + 991*T^13 + 16584*T^12 + 112153*T^11 + 1306214*T^10 + 9519319*T^9 + 95073056*T^8 + 635668019*T^7 + 4408033141*T^6 + 20477207159*T^5 + 89071952001*T^4 + 301348671624*T^3 + 927480123776*T^2 + 725848066048*T + 233420394496
$79$
\( T^{16} - 14 T^{15} + \cdots + 8008281121 \)
T^16 - 14*T^15 + 396*T^14 - 6778*T^13 + 95164*T^12 - 786040*T^11 + 5204998*T^10 - 15704676*T^9 + 99403903*T^8 - 771141274*T^7 + 8966017598*T^6 - 46660662450*T^5 + 150687600039*T^4 + 4975271218*T^3 + 365698267121*T^2 - 87468696336*T + 8008281121
$83$
\( T^{16} - 20 T^{15} + \cdots + 129413376 \)
T^16 - 20*T^15 + 279*T^14 - 1944*T^13 + 42534*T^12 + 31628*T^11 + 3219804*T^10 + 15638204*T^9 + 169809521*T^8 + 330151904*T^7 + 5288373976*T^6 + 2391581984*T^5 + 31431785776*T^4 - 45812049216*T^3 + 26457627456*T^2 - 2922175872*T + 129413376
$89$
\( T^{16} + 13 T^{15} + \cdots + 19\!\cdots\!76 \)
T^16 + 13*T^15 + 456*T^14 + 4659*T^13 + 102231*T^12 + 882739*T^11 + 15368016*T^10 + 113750689*T^9 + 3422920021*T^8 + 33096601644*T^7 + 359836830144*T^6 + 1392871188168*T^5 + 6148830526704*T^4 - 13948482999744*T^3 + 267257691281664*T^2 - 1016182561397760*T + 1992678175051776
$97$
\( T^{16} - 55 T^{15} + \cdots + 15953601686416 \)
T^16 - 55*T^15 + 1789*T^14 - 37634*T^13 + 584654*T^12 - 6183397*T^11 + 47629399*T^10 - 168794431*T^9 + 232010206*T^8 + 1828816974*T^7 + 72193698241*T^6 - 513703069761*T^5 + 2587259823781*T^4 + 23357843892524*T^3 + 64298624972136*T^2 + 24916345847048*T + 15953601686416
show more
show less