[N,k,chi] = [201,2,Mod(37,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("201.37");
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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\)
\(68\)
\(136\)
\(\chi(n)\)
\(1\)
\(-\beta_{4}\)
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
\( T_{2}^{10} + 2T_{2}^{9} + 10T_{2}^{8} + 8T_{2}^{7} + 49T_{2}^{6} + 39T_{2}^{5} + 128T_{2}^{4} + 14T_{2}^{3} + 119T_{2}^{2} + 49T_{2} + 49 \)
T2^10 + 2*T2^9 + 10*T2^8 + 8*T2^7 + 49*T2^6 + 39*T2^5 + 128*T2^4 + 14*T2^3 + 119*T2^2 + 49*T2 + 49
acting on \(S_{2}^{\mathrm{new}}(201, [\chi])\).
$p$
$F_p(T)$
$2$
\( T^{10} + 2 T^{9} + 10 T^{8} + 8 T^{7} + \cdots + 49 \)
T^10 + 2*T^9 + 10*T^8 + 8*T^7 + 49*T^6 + 39*T^5 + 128*T^4 + 14*T^3 + 119*T^2 + 49*T + 49
$3$
\( (T + 1)^{10} \)
(T + 1)^10
$5$
\( (T^{5} - T^{4} - 12 T^{3} + 13 T^{2} + 12 T - 12)^{2} \)
(T^5 - T^4 - 12*T^3 + 13*T^2 + 12*T - 12)^2
$7$
\( T^{10} + T^{9} + 30 T^{8} + 51 T^{7} + \cdots + 33489 \)
T^10 + T^9 + 30*T^8 + 51*T^7 + 761*T^6 + 1103*T^5 + 4897*T^4 + 5814*T^3 + 21720*T^2 + 21960*T + 33489
$11$
\( T^{10} - 2 T^{9} + 25 T^{8} + 14 T^{7} + \cdots + 576 \)
T^10 - 2*T^9 + 25*T^8 + 14*T^7 + 433*T^6 - 174*T^5 + 904*T^4 - 504*T^3 + 1632*T^2 - 864*T + 576
$13$
\( T^{10} - 3 T^{9} + 42 T^{8} - 57 T^{7} + \cdots + 169 \)
T^10 - 3*T^9 + 42*T^8 - 57*T^7 + 1337*T^6 - 2671*T^5 + 5583*T^4 - 1950*T^3 + 1210*T^2 + 182*T + 169
$17$
\( T^{10} - 2 T^{9} + 40 T^{8} + \cdots + 219961 \)
T^10 - 2*T^9 + 40*T^8 - 50*T^7 + 1117*T^6 - 1461*T^5 + 13619*T^4 - 15407*T^3 + 119210*T^2 - 141169*T + 219961
$19$
\( T^{10} - 3 T^{9} + 32 T^{8} + \cdots + 4489 \)
T^10 - 3*T^9 + 32*T^8 + 17*T^7 + 545*T^6 - 293*T^5 + 1901*T^4 - 1470*T^3 + 5586*T^2 - 4154*T + 4489
$23$
\( T^{10} + T^{9} + 31 T^{8} - 18 T^{7} + \cdots + 3481 \)
T^10 + T^9 + 31*T^8 - 18*T^7 + 717*T^6 - 257*T^5 + 5765*T^4 - 4674*T^3 + 35367*T^2 - 11151*T + 3481
$29$
\( T^{10} - 12 T^{9} + 180 T^{8} + \cdots + 20421361 \)
T^10 - 12*T^9 + 180*T^8 - 1002*T^7 + 10835*T^6 - 52771*T^5 + 426201*T^4 - 995763*T^3 + 4114348*T^2 + 4225265*T + 20421361
$31$
\( T^{10} + 12 T^{9} + 109 T^{8} + \cdots + 4096 \)
T^10 + 12*T^9 + 109*T^8 + 444*T^7 + 1497*T^6 + 2588*T^5 + 5392*T^4 + 6016*T^3 + 15616*T^2 + 8192*T + 4096
$37$
\( T^{10} - 27 T^{9} + \cdots + 381303729 \)
T^10 - 27*T^9 + 520*T^8 - 5831*T^7 + 53047*T^6 - 329539*T^5 + 1963117*T^4 - 8804118*T^3 + 44786046*T^2 - 133330356*T + 381303729
$41$
\( T^{10} + 7 T^{9} + 140 T^{8} + \cdots + 53275401 \)
T^10 + 7*T^9 + 140*T^8 + 579*T^7 + 11193*T^6 + 43811*T^5 + 440875*T^4 + 511266*T^3 + 6244128*T^2 + 9809856*T + 53275401
$43$
\( (T^{5} - 6 T^{4} - 171 T^{3} + 1117 T^{2} + \cdots - 41232)^{2} \)
(T^5 - 6*T^4 - 171*T^3 + 1117*T^2 + 6192*T - 41232)^2
$47$
\( T^{10} + 33 T^{9} + 702 T^{8} + \cdots + 32867289 \)
T^10 + 33*T^9 + 702*T^8 + 9179*T^7 + 88821*T^6 + 578439*T^5 + 2764645*T^4 + 7454622*T^3 + 13118868*T^2 - 9631440*T + 32867289
$53$
\( (T^{5} + 12 T^{4} - 89 T^{3} - 1745 T^{2} + \cdots - 9476)^{2} \)
(T^5 + 12*T^4 - 89*T^3 - 1745*T^2 - 7504*T - 9476)^2
$59$
\( (T^{5} - 12 T^{4} - 67 T^{3} + 1039 T^{2} + \cdots - 3792)^{2} \)
(T^5 - 12*T^4 - 67*T^3 + 1039*T^2 - 1560*T - 3792)^2
$61$
\( T^{10} - T^{9} + 150 T^{8} + \cdots + 166590649 \)
T^10 - T^9 + 150*T^8 + 789*T^7 + 17855*T^6 + 68639*T^5 + 715181*T^4 + 2557966*T^3 + 20338916*T^2 + 51963582*T + 166590649
$67$
\( T^{10} - 2 T^{9} + \cdots + 1350125107 \)
T^10 - 2*T^9 - 84*T^8 + 293*T^7 + 3191*T^6 - 37614*T^5 + 213797*T^4 + 1315277*T^3 - 25264092*T^2 - 40302242*T + 1350125107
$71$
\( T^{10} + T^{9} + 199 T^{8} + \cdots + 379041961 \)
T^10 + T^9 + 199*T^8 + 406*T^7 + 29773*T^6 + 59799*T^5 + 1998869*T^4 + 4770358*T^3 + 100610927*T^2 + 189491777*T + 379041961
$73$
\( T^{10} - 12 T^{9} + \cdots + 3692871361 \)
T^10 - 12*T^9 + 370*T^8 - 1710*T^7 + 67197*T^6 - 310591*T^5 + 6512179*T^4 - 4448867*T^3 + 242749180*T^2 - 632666059*T + 3692871361
$79$
\( T^{10} - 7 T^{9} + 108 T^{8} + \cdots + 187489 \)
T^10 - 7*T^9 + 108*T^8 + 321*T^7 + 3341*T^6 + 4187*T^5 + 32405*T^4 + 72346*T^3 + 193526*T^2 + 200046*T + 187489
$83$
\( T^{10} - 12 T^{9} + 138 T^{8} - 126 T^{7} + \cdots + 1 \)
T^10 - 12*T^9 + 138*T^8 - 126*T^7 + 347*T^6 + 475*T^5 + 663*T^4 + 339*T^3 + 142*T^2 + 13*T + 1
$89$
\( (T^{5} - 6 T^{4} - 49 T^{3} + 227 T^{2} + \cdots + 156)^{2} \)
(T^5 - 6*T^4 - 49*T^3 + 227*T^2 + 432*T + 156)^2
$97$
\( T^{10} + 9 T^{9} + 192 T^{8} + \cdots + 23902321 \)
T^10 + 9*T^9 + 192*T^8 + 1641*T^7 + 26645*T^6 + 195401*T^5 + 1427115*T^4 + 4311438*T^3 + 12426616*T^2 - 11948716*T + 23902321
show more
show less