[N,k,chi] = [950,2,Mod(101,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.101");
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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\)
\(77\)
\(401\)
\(\chi(n)\)
\(1\)
\(-\beta_{7}\)
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
\( T_{3}^{12} - 9T_{3}^{10} + 36T_{3}^{8} + 64T_{3}^{6} + 189T_{3}^{4} + 999T_{3}^{2} + 1369 \)
T3^12 - 9*T3^10 + 36*T3^8 + 64*T3^6 + 189*T3^4 + 999*T3^2 + 1369
acting on \(S_{2}^{\mathrm{new}}(950, [\chi])\).
$p$
$F_p(T)$
$2$
\( (T^{6} + T^{3} + 1)^{2} \)
(T^6 + T^3 + 1)^2
$3$
\( T^{12} - 9 T^{10} + 36 T^{8} + \cdots + 1369 \)
T^12 - 9*T^10 + 36*T^8 + 64*T^6 + 189*T^4 + 999*T^2 + 1369
$5$
\( T^{12} \)
T^12
$7$
\( T^{12} + 6 T^{11} + 48 T^{10} + \cdots + 23104 \)
T^12 + 6*T^11 + 48*T^10 + 104*T^9 + 612*T^8 + 648*T^7 + 6288*T^6 + 1296*T^5 + 29232*T^4 - 8032*T^3 + 106464*T^2 - 47424*T + 23104
$11$
\( T^{12} - 6 T^{11} + 54 T^{10} - 84 T^{9} + \cdots + 729 \)
T^12 - 6*T^11 + 54*T^10 - 84*T^9 + 765*T^8 - 324*T^7 + 10404*T^6 + 5022*T^5 + 39447*T^4 - 34344*T^3 + 43011*T^2 - 5832*T + 729
$13$
\( T^{12} + 6 T^{11} + 6 T^{10} + \cdots + 46656 \)
T^12 + 6*T^11 + 6*T^10 - 8*T^9 - 60*T^8 - 1032*T^7 - 944*T^6 + 13536*T^5 + 63072*T^4 + 114912*T^3 + 132192*T^2 + 93312*T + 46656
$17$
\( T^{12} - 18 T^{11} + 108 T^{10} + \cdots + 12766329 \)
T^12 - 18*T^11 + 108*T^10 + 100*T^9 - 4104*T^8 + 14202*T^7 + 45091*T^6 - 523926*T^5 + 2135304*T^4 - 5393700*T^3 + 9453348*T^2 - 4952178*T + 12766329
$19$
\( T^{12} - 6 T^{10} + 162 T^{9} + \cdots + 47045881 \)
T^12 - 6*T^10 + 162*T^9 + 312*T^8 + 270*T^7 + 12913*T^6 + 5130*T^5 + 112632*T^4 + 1111158*T^3 - 781926*T^2 + 47045881
$23$
\( T^{12} - 30 T^{11} + 462 T^{10} + \cdots + 1871424 \)
T^12 - 30*T^11 + 462*T^10 - 4600*T^9 + 33360*T^8 - 181896*T^7 + 746704*T^6 - 2318256*T^5 + 5436864*T^4 - 9151776*T^3 + 10051776*T^2 - 6303744*T + 1871424
$29$
\( T^{12} + 6 T^{11} + 60 T^{10} + \cdots + 5184 \)
T^12 + 6*T^11 + 60*T^10 + 748*T^9 + 1776*T^8 + 6384*T^7 + 221392*T^6 - 246096*T^5 + 10647648*T^4 - 3327552*T^3 + 313632*T^2 + 103680*T + 5184
$31$
\( T^{12} - 6 T^{11} + 108 T^{10} + \cdots + 23104 \)
T^12 - 6*T^11 + 108*T^10 - 432*T^9 + 6492*T^8 - 23424*T^7 + 233008*T^6 - 559056*T^5 + 4998096*T^4 - 10054080*T^3 + 59526816*T^2 - 1174656*T + 23104
$37$
\( (T^{6} + 18 T^{5} + 48 T^{4} - 560 T^{3} + \cdots - 2168)^{2} \)
(T^6 + 18*T^5 + 48*T^4 - 560*T^3 - 2844*T^2 - 4368*T - 2168)^2
$41$
\( T^{12} + 6 T^{11} + 93 T^{10} + \cdots + 114896961 \)
T^12 + 6*T^11 + 93*T^10 + 332*T^9 - 1668*T^8 + 27084*T^7 + 248374*T^6 - 321570*T^5 + 5461668*T^4 + 1481112*T^3 - 17953812*T^2 + 41675472*T + 114896961
$43$
\( T^{12} - 30 T^{10} + 340 T^{9} + \cdots + 12341169 \)
T^12 - 30*T^10 + 340*T^9 + 816*T^8 - 1428*T^7 + 185821*T^6 - 1412700*T^5 + 7564356*T^4 - 12206748*T^3 + 64800306*T^2 - 51598944*T + 12341169
$47$
\( T^{12} - 6 T^{11} + 108 T^{10} + \cdots + 16842816 \)
T^12 - 6*T^11 + 108*T^10 + 60*T^9 - 2880*T^8 + 23760*T^7 + 134928*T^6 - 151632*T^5 + 899424*T^4 + 876096*T^3 - 1796256*T^2 + 7091712*T + 16842816
$53$
\( T^{12} - 12 T^{11} + 90 T^{10} + \cdots + 46656 \)
T^12 - 12*T^11 + 90*T^10 - 168*T^9 - 15624*T^8 + 80136*T^7 + 1397232*T^6 + 1881792*T^5 + 19176912*T^4 - 19048608*T^3 + 8281440*T^2 - 933120*T + 46656
$59$
\( T^{12} + 24 T^{11} + \cdots + 3234310641 \)
T^12 + 24*T^11 + 219*T^10 + 440*T^9 + 3138*T^8 + 106320*T^7 + 1162072*T^6 + 9116352*T^5 + 34271730*T^4 - 338533596*T^3 + 617009724*T^2 - 1032891102*T + 3234310641
$61$
\( T^{12} + 30 T^{11} + \cdots + 224041024 \)
T^12 + 30*T^11 + 510*T^10 + 5992*T^9 + 57744*T^8 + 426744*T^7 + 2327664*T^6 + 8342064*T^5 + 20139264*T^4 + 11464288*T^3 - 80018880*T^2 - 97711104*T + 224041024
$67$
\( T^{12} + 12 T^{11} - 135 T^{10} + \cdots + 2859481 \)
T^12 + 12*T^11 - 135*T^10 - 792*T^9 + 23886*T^8 - 18060*T^7 - 215000*T^6 - 1601004*T^5 + 5002659*T^4 + 6725088*T^3 + 125542143*T^2 + 6716652*T + 2859481
$71$
\( T^{12} + 42 T^{11} + \cdots + 6701714496 \)
T^12 + 42*T^11 + 702*T^10 + 5736*T^9 + 27792*T^8 + 147960*T^7 + 1221840*T^6 + 4521744*T^5 + 26754624*T^4 + 176823648*T^3 + 518114880*T^2 + 1520705664*T + 6701714496
$73$
\( T^{12} + 6 T^{11} + 6 T^{10} + \cdots + 136258929 \)
T^12 + 6*T^11 + 6*T^10 - 746*T^9 - 4299*T^8 - 9636*T^7 + 586819*T^6 + 5265990*T^5 + 31256532*T^4 + 178257600*T^3 + 573942753*T^2 + 420648228*T + 136258929
$79$
\( T^{12} - 60 T^{11} + \cdots + 1036324864 \)
T^12 - 60*T^11 + 1860*T^10 - 38432*T^9 + 563904*T^8 - 5787072*T^7 + 39627840*T^6 - 165814272*T^5 + 385198848*T^4 - 366187520*T^3 + 503758848*T^2 + 1897525248*T + 1036324864
$83$
\( T^{12} + 24 T^{11} + \cdots + 51075548001 \)
T^12 + 24*T^11 + 564*T^10 + 7112*T^9 + 105819*T^8 + 1098168*T^7 + 12443122*T^6 + 86649156*T^5 + 554019813*T^4 + 1605585744*T^3 + 5382935109*T^2 - 602061336*T + 51075548001
$89$
\( T^{12} + 12 T^{11} - 120 T^{10} + \cdots + 2653641 \)
T^12 + 12*T^11 - 120*T^10 - 3070*T^9 - 240*T^8 + 307320*T^7 + 2151703*T^6 + 4663656*T^5 + 6984288*T^4 + 7028442*T^3 + 7649640*T^2 + 3225420*T + 2653641
$97$
\( T^{12} + 30 T^{11} + \cdots + 2521747089 \)
T^12 + 30*T^11 + 333*T^10 + 1078*T^9 - 9006*T^8 - 99000*T^7 - 182324*T^6 + 2427096*T^5 + 26697609*T^4 + 133565982*T^3 + 440892243*T^2 + 703238868*T + 2521747089
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