gp: [N,k,chi] = [4205,2,Mod(1,4205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
sage: from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4205, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
magma: //Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4205.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Newform invariants
sage: traces = [24,0,0]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
gp: f = lf[1] \\ Warning: the index may be different
The algebraic q q q -expansion of this newform has not been computed, but we have computed the trace expansion .
For each embedding ι m \iota_m ι m of the coefficient field, the values ι m ( a n ) \iota_m(a_n) ι m ( a n ) are shown below.
For more information on an embedded modular form you can click on its label.
gp: mfembed(f)
Refresh table
p p p
Sign
5 5 5
− 1 -1 − 1
29 29 2 9
− 1 -1 − 1
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on S 2 n e w ( Γ 0 ( 4205 ) ) S_{2}^{\mathrm{new}}(\Gamma_0(4205)) S 2 n e w ( Γ 0 ( 4 2 0 5 ) ) :
T 2 24 − 31 T 2 22 + 414 T 2 20 − 3129 T 2 18 + 14790 T 2 16 − 45609 T 2 14 + ⋯ + 1 T_{2}^{24} - 31 T_{2}^{22} + 414 T_{2}^{20} - 3129 T_{2}^{18} + 14790 T_{2}^{16} - 45609 T_{2}^{14} + \cdots + 1 T 2 2 4 − 3 1 T 2 2 2 + 4 1 4 T 2 2 0 − 3 1 2 9 T 2 1 8 + 1 4 7 9 0 T 2 1 6 − 4 5 6 0 9 T 2 1 4 + ⋯ + 1
T2^24 - 31*T2^22 + 414*T2^20 - 3129*T2^18 + 14790*T2^16 - 45609*T2^14 + 92854*T2^12 - 123288*T2^10 + 102402*T2^8 - 48363*T2^6 + 10158*T2^4 - 199*T2^2 + 1
T 3 24 − 45 T 3 22 + 845 T 3 20 − 8613 T 3 18 + 52013 T 3 16 − 191573 T 3 14 + ⋯ + 169 T_{3}^{24} - 45 T_{3}^{22} + 845 T_{3}^{20} - 8613 T_{3}^{18} + 52013 T_{3}^{16} - 191573 T_{3}^{14} + \cdots + 169 T 3 2 4 − 4 5 T 3 2 2 + 8 4 5 T 3 2 0 − 8 6 1 3 T 3 1 8 + 5 2 0 1 3 T 3 1 6 − 1 9 1 5 7 3 T 3 1 4 + ⋯ + 1 6 9
T3^24 - 45*T3^22 + 845*T3^20 - 8613*T3^18 + 52013*T3^16 - 191573*T3^14 + 432173*T3^12 - 595737*T3^10 + 491861*T3^8 - 230569*T3^6 + 54977*T3^4 - 5501*T3^2 + 169