Properties

 Label 3040.2.e.a Level $3040$ Weight $2$ Character orbit 3040.e Analytic conductor $24.275$ Analytic rank $0$ Dimension $80$ CM no Inner twists $4$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3040,2,Mod(911,3040)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3040, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3040.911");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$3040 = 2^{5} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3040.e (of order $$2$$, degree $$1$$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$24.2745222145$$ Analytic rank: $$0$$ Dimension: $$80$$ Twist minimal: no (minimal twist has level 760) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic $$q$$-expansion, but we have computed the trace expansion.

 $$\operatorname{Tr}(f)(q) =$$ $$80 q - 80 q^{9}+O(q^{10})$$ 80 * q - 80 * q^9 $$\operatorname{Tr}(f)(q) =$$ $$80 q - 80 q^{9} - 8 q^{19} - 80 q^{25} - 112 q^{49} - 8 q^{57} - 32 q^{73} + 96 q^{81} + 32 q^{99}+O(q^{100})$$ 80 * q - 80 * q^9 - 8 * q^19 - 80 * q^25 - 112 * q^49 - 8 * q^57 - 32 * q^73 + 96 * q^81 + 32 * q^99

Embeddings

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.

comment: embeddings in the coefficient field

gp: mfembed(f)

Label   $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
911.1 0 3.34453i 0 1.00000i 0 3.87119i 0 −8.18585 0
911.2 0 3.34453i 0 1.00000i 0 3.87119i 0 −8.18585 0
911.3 0 3.23880i 0 1.00000i 0 0.457390i 0 −7.48983 0
911.4 0 3.23880i 0 1.00000i 0 0.457390i 0 −7.48983 0
911.5 0 2.99395i 0 1.00000i 0 3.07859i 0 −5.96377 0
911.6 0 2.99395i 0 1.00000i 0 3.07859i 0 −5.96377 0
911.7 0 2.70495i 0 1.00000i 0 3.65554i 0 −4.31673 0
911.8 0 2.70495i 0 1.00000i 0 3.65554i 0 −4.31673 0
911.9 0 2.56963i 0 1.00000i 0 2.10549i 0 −3.60298 0
911.10 0 2.56963i 0 1.00000i 0 2.10549i 0 −3.60298 0
911.11 0 2.46872i 0 1.00000i 0 2.44811i 0 −3.09460 0
911.12 0 2.46872i 0 1.00000i 0 2.44811i 0 −3.09460 0
911.13 0 2.38464i 0 1.00000i 0 4.57467i 0 −2.68651 0
911.14 0 2.38464i 0 1.00000i 0 4.57467i 0 −2.68651 0
911.15 0 2.25164i 0 1.00000i 0 0.940149i 0 −2.06991 0
911.16 0 2.25164i 0 1.00000i 0 0.940149i 0 −2.06991 0
911.17 0 2.07809i 0 1.00000i 0 0.0366154i 0 −1.31848 0
911.18 0 2.07809i 0 1.00000i 0 0.0366154i 0 −1.31848 0
911.19 0 2.06995i 0 1.00000i 0 4.61911i 0 −1.28468 0
911.20 0 2.06995i 0 1.00000i 0 4.61911i 0 −1.28468 0
See all 80 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 911.80 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.d odd 2 1 inner
19.b odd 2 1 inner
152.b even 2 1 inner

Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 3040.2.e.a 80
4.b odd 2 1 760.2.e.a 80
8.b even 2 1 760.2.e.a 80
8.d odd 2 1 inner 3040.2.e.a 80
19.b odd 2 1 inner 3040.2.e.a 80
76.d even 2 1 760.2.e.a 80
152.b even 2 1 inner 3040.2.e.a 80
152.g odd 2 1 760.2.e.a 80

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
760.2.e.a 80 4.b odd 2 1
760.2.e.a 80 8.b even 2 1
760.2.e.a 80 76.d even 2 1
760.2.e.a 80 152.g odd 2 1
3040.2.e.a 80 1.a even 1 1 trivial
3040.2.e.a 80 8.d odd 2 1 inner
3040.2.e.a 80 19.b odd 2 1 inner
3040.2.e.a 80 152.b even 2 1 inner

Hecke kernels

This newform subspace is the entire newspace $$S_{2}^{\mathrm{new}}(3040, [\chi])$$.