[N,k,chi] = [149,2,Mod(1,149)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(149, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("149.1");
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
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
\(149\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{9} + T_{2}^{8} - 15T_{2}^{7} - 12T_{2}^{6} + 75T_{2}^{5} + 48T_{2}^{4} - 137T_{2}^{3} - 76T_{2}^{2} + 68T_{2} + 39 \)
T2^9 + T2^8 - 15*T2^7 - 12*T2^6 + 75*T2^5 + 48*T2^4 - 137*T2^3 - 76*T2^2 + 68*T2 + 39
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(149))\).
$p$
$F_p(T)$
$2$
\( T^{9} + T^{8} - 15 T^{7} - 12 T^{6} + \cdots + 39 \)
T^9 + T^8 - 15*T^7 - 12*T^6 + 75*T^5 + 48*T^4 - 137*T^3 - 76*T^2 + 68*T + 39
$3$
\( T^{9} - 6 T^{8} + 55 T^{6} - 67 T^{5} + \cdots + 27 \)
T^9 - 6*T^8 + 55*T^6 - 67*T^5 - 125*T^4 + 235*T^3 - 6*T^2 - 117*T + 27
$5$
\( T^{9} + T^{8} - 25 T^{7} - 4 T^{6} + \cdots - 221 \)
T^9 + T^8 - 25*T^7 - 4*T^6 + 202*T^5 - 83*T^4 - 529*T^3 + 305*T^2 + 392*T - 221
$7$
\( T^{9} - 3 T^{8} - 34 T^{7} + 117 T^{6} + \cdots - 64 \)
T^9 - 3*T^8 - 34*T^7 + 117*T^6 + 208*T^5 - 916*T^4 + 144*T^3 + 1056*T^2 - 128*T - 64
$11$
\( T^{9} - 5 T^{8} - 33 T^{7} + 202 T^{6} + \cdots + 981 \)
T^9 - 5*T^8 - 33*T^7 + 202*T^6 + 66*T^5 - 1503*T^4 + 997*T^3 + 2817*T^2 - 3392*T + 981
$13$
\( T^{9} - 7 T^{8} - 28 T^{7} + 277 T^{6} + \cdots - 64 \)
T^9 - 7*T^8 - 28*T^7 + 277*T^6 - 152*T^5 - 2028*T^4 + 3072*T^3 + 32*T^2 - 512*T - 64
$17$
\( T^{9} + 5 T^{8} - 75 T^{7} + \cdots + 24053 \)
T^9 + 5*T^8 - 75*T^7 - 342*T^6 + 1572*T^5 + 7471*T^4 - 7485*T^3 - 53675*T^2 - 36298*T + 24053
$19$
\( T^{9} - 30 T^{8} + 337 T^{7} + \cdots + 145856 \)
T^9 - 30*T^8 + 337*T^7 - 1533*T^6 - 768*T^5 + 38360*T^4 - 171648*T^3 + 358384*T^2 - 366592*T + 145856
$23$
\( T^{9} + 4 T^{8} - 88 T^{7} + \cdots - 6341 \)
T^9 + 4*T^8 - 88*T^7 - 135*T^6 + 2377*T^5 - 1281*T^4 - 10871*T^3 + 5476*T^2 + 11587*T - 6341
$29$
\( T^{9} + 16 T^{8} + 52 T^{7} + \cdots + 2861 \)
T^9 + 16*T^8 + 52*T^7 - 397*T^6 - 3233*T^5 - 7917*T^4 - 6043*T^3 + 3944*T^2 + 7739*T + 2861
$31$
\( T^{9} - 22 T^{8} + 91 T^{7} + \cdots + 161984 \)
T^9 - 22*T^8 + 91*T^7 + 991*T^6 - 7564*T^5 - 3356*T^4 + 98336*T^3 - 32960*T^2 - 312448*T + 161984
$37$
\( T^{9} + 7 T^{8} - 142 T^{7} + \cdots - 75969 \)
T^9 + 7*T^8 - 142*T^7 - 828*T^6 + 5789*T^5 + 18971*T^4 - 88867*T^3 + 40715*T^2 + 104171*T - 75969
$41$
\( T^{9} - 6 T^{8} - 185 T^{7} + \cdots + 35328 \)
T^9 - 6*T^8 - 185*T^7 + 1007*T^6 + 9700*T^5 - 40160*T^4 - 155136*T^3 + 317376*T^2 - 186112*T + 35328
$43$
\( T^{9} - 4 T^{8} - 202 T^{7} + \cdots + 109051 \)
T^9 - 4*T^8 - 202*T^7 + 423*T^6 + 10581*T^5 + 9877*T^4 - 113871*T^3 - 256632*T^2 - 68795*T + 109051
$47$
\( T^{9} + 6 T^{8} - 273 T^{7} + \cdots + 1225536 \)
T^9 + 6*T^8 - 273*T^7 - 1593*T^6 + 21800*T^5 + 134552*T^4 - 414736*T^3 - 3462160*T^2 - 4525952*T + 1225536
$53$
\( T^{9} + 2 T^{8} - 170 T^{7} + \cdots - 43997 \)
T^9 + 2*T^8 - 170*T^7 - 1081*T^6 + 4013*T^5 + 59133*T^4 + 216201*T^3 + 327714*T^2 + 153685*T - 43997
$59$
\( T^{9} - 43 T^{8} + 711 T^{7} + \cdots - 13589 \)
T^9 - 43*T^8 + 711*T^7 - 5710*T^6 + 23024*T^5 - 40699*T^4 + 4089*T^3 + 67513*T^2 - 45344*T - 13589
$61$
\( T^{9} - T^{8} - 191 T^{7} + \cdots + 1028703 \)
T^9 - T^8 - 191*T^7 + 246*T^6 + 11156*T^5 - 10667*T^4 - 200993*T^3 - 122141*T^2 + 830518*T + 1028703
$67$
\( T^{9} - 33 T^{8} + 162 T^{7} + \cdots - 8246976 \)
T^9 - 33*T^8 + 162*T^7 + 4853*T^6 - 59204*T^5 + 97700*T^4 + 1357024*T^3 - 7316416*T^2 + 13408448*T - 8246976
$71$
\( T^{9} - 15 T^{8} - 55 T^{7} + \cdots + 2931 \)
T^9 - 15*T^8 - 55*T^7 + 1188*T^6 - 1656*T^5 - 17961*T^4 + 52241*T^3 - 8251*T^2 - 51176*T + 2931
$73$
\( T^{9} + 11 T^{8} - 145 T^{7} + \cdots - 3257073 \)
T^9 + 11*T^8 - 145*T^7 - 2102*T^6 + 706*T^5 + 89825*T^4 + 247339*T^3 - 714453*T^2 - 3446560*T - 3257073
$79$
\( T^{9} - T^{8} - 549 T^{7} + \cdots + 468778432 \)
T^9 - T^8 - 549*T^7 + 173*T^6 + 106772*T^5 + 52012*T^4 - 8541904*T^3 - 11412320*T^2 + 225852288*T + 468778432
$83$
\( T^{9} + 4 T^{8} - 384 T^{7} + \cdots + 2245797 \)
T^9 + 4*T^8 - 384*T^7 - 1765*T^6 + 42213*T^5 + 217533*T^4 - 1021329*T^3 - 5009504*T^2 - 3680845*T + 2245797
$89$
\( T^{9} + 19 T^{8} - 37 T^{7} + \cdots - 239936 \)
T^9 + 19*T^8 - 37*T^7 - 1467*T^6 + 2336*T^5 + 33412*T^4 - 103920*T^3 - 16720*T^2 + 313344*T - 239936
$97$
\( T^{9} + T^{8} - 462 T^{7} + \cdots + 3173696 \)
T^9 + T^8 - 462*T^7 + 79*T^6 + 50736*T^5 + 9648*T^4 - 1868176*T^3 - 930512*T^2 + 17893120*T + 3173696
show more
show less