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Properties

Label 7524.2.f.a
Level $7524$
Weight $2$
Character orbit 7524.f
Analytic conductor $60.079$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7524,2,Mod(4445,7524)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7524, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("7524.4445");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7524 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7524.f (of order \(2\), degree \(1\), 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: \(60.0794424808\)
Analytic rank: \(0\)
Dimension: \(64\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 64 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 64 q + 8 q^{19} - 48 q^{25} - 16 q^{43} + 16 q^{49} + 16 q^{61} + 64 q^{73} - 64 q^{85}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
4445.1 0 0 0 − 4.39537i 0 −1.59577 0 0 0
4445.2 0 0 0 4.39537i 0 −1.59577 0 0 0
4445.3 0 0 0 − 2.31011i 0 −2.35073 0 0 0
4445.4 0 0 0 2.31011i 0 −2.35073 0 0 0
4445.5 0 0 0 − 1.84580i 0 −3.63173 0 0 0
4445.6 0 0 0 1.84580i 0 −3.63173 0 0 0
4445.7 0 0 0 − 3.38823i 0 0.570518 0 0 0
4445.8 0 0 0 3.38823i 0 0.570518 0 0 0
4445.9 0 0 0 − 2.28363i 0 −3.78099 0 0 0
4445.10 0 0 0 2.28363i 0 −3.78099 0 0 0
4445.11 0 0 0 − 2.95067i 0 4.47058 0 0 0
4445.12 0 0 0 2.95067i 0 4.47058 0 0 0
4445.13 0 0 0 − 0.159971i 0 2.87805 0 0 0
4445.14 0 0 0 0.159971i 0 2.87805 0 0 0
4445.15 0 0 0 − 2.83674i 0 −3.88228 0 0 0
4445.16 0 0 0 2.83674i 0 −3.88228 0 0 0
4445.17 0 0 0 − 0.0330473i 0 0.0761015 0 0 0
4445.18 0 0 0 0.0330473i 0 0.0761015 0 0 0
4445.19 0 0 0 − 0.777747i 0 −2.62576 0 0 0
4445.20 0 0 0 0.777747i 0 −2.62576 0 0 0
See all 64 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 4445.64
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 7524.2.f.a ✓ 64
3.b odd 2 1 inner 7524.2.f.a ✓ 64
19.b odd 2 1 inner 7524.2.f.a ✓ 64
57.d even 2 1 inner 7524.2.f.a ✓ 64
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
7524.2.f.a ✓ 64 1.a even 1 1 trivial
7524.2.f.a ✓ 64 3.b odd 2 1 inner
7524.2.f.a ✓ 64 19.b odd 2 1 inner
7524.2.f.a ✓ 64 57.d even 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(7524, [\chi])\).