↑

Properties

Label 276.4.g.a
Level $276$
Weight $4$
Character orbit 276.g
Analytic conductor $16.285$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [276,4,Mod(137,276)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(276, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("276.137");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 276.g (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: \(16.2845271616\)
Analytic rank: \(0\)
Dimension: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{3} - 60 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{3} - 60 q^{9} - 48 q^{13} + 720 q^{25} - 316 q^{27} + 288 q^{31} + 432 q^{39} - 504 q^{49} - 672 q^{55} + 472 q^{69} + 1920 q^{73} + 1580 q^{75} - 1204 q^{81} - 3768 q^{85} + 3856 q^{87} - 1844 q^{93}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
137.1 0 −4.86581 − 1.82315i 0 −10.3377 0 22.6406i 0 20.3523 + 17.7422i 0
137.2 0 −4.86581 − 1.82315i 0 10.3377 0 − 22.6406i 0 20.3523 + 17.7422i 0
137.3 0 −4.86581 + 1.82315i 0 −10.3377 0 − 22.6406i 0 20.3523 − 17.7422i 0
137.4 0 −4.86581 + 1.82315i 0 10.3377 0 22.6406i 0 20.3523 − 17.7422i 0
137.5 0 −3.90548 − 3.42743i 0 −15.0498 0 − 16.4104i 0 3.50550 + 26.7715i 0
137.6 0 −3.90548 − 3.42743i 0 15.0498 0 16.4104i 0 3.50550 + 26.7715i 0
137.7 0 −3.90548 + 3.42743i 0 −15.0498 0 16.4104i 0 3.50550 − 26.7715i 0
137.8 0 −3.90548 + 3.42743i 0 15.0498 0 − 16.4104i 0 3.50550 − 26.7715i 0
137.9 0 −1.24067 − 5.04586i 0 −4.29456 0 − 7.44830i 0 −23.9215 + 12.5205i 0
137.10 0 −1.24067 − 5.04586i 0 4.29456 0 7.44830i 0 −23.9215 + 12.5205i 0
137.11 0 −1.24067 + 5.04586i 0 −4.29456 0 7.44830i 0 −23.9215 − 12.5205i 0
137.12 0 −1.24067 + 5.04586i 0 4.29456 0 − 7.44830i 0 −23.9215 − 12.5205i 0
137.13 0 1.37849 − 5.00997i 0 −6.91682 0 − 23.7997i 0 −23.1995 − 13.8124i 0
137.14 0 1.37849 − 5.00997i 0 6.91682 0 23.7997i 0 −23.1995 − 13.8124i 0
137.15 0 1.37849 + 5.00997i 0 −6.91682 0 23.7997i 0 −23.1995 + 13.8124i 0
137.16 0 1.37849 + 5.00997i 0 6.91682 0 − 23.7997i 0 −23.1995 + 13.8124i 0
137.17 0 2.81754 − 4.36594i 0 −21.4867 0 23.0899i 0 −11.1229 − 24.6025i 0
137.18 0 2.81754 − 4.36594i 0 21.4867 0 − 23.0899i 0 −11.1229 − 24.6025i 0
137.19 0 2.81754 + 4.36594i 0 −21.4867 0 − 23.0899i 0 −11.1229 + 24.6025i 0
137.20 0 2.81754 + 4.36594i 0 21.4867 0 23.0899i 0 −11.1229 + 24.6025i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 137.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
23.b odd 2 1 inner
69.c even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 276.4.g.a ✓ 24
3.b odd 2 1 inner 276.4.g.a ✓ 24
23.b odd 2 1 inner 276.4.g.a ✓ 24
69.c even 2 1 inner 276.4.g.a ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
276.4.g.a ✓ 24 1.a even 1 1 trivial
276.4.g.a ✓ 24 3.b odd 2 1 inner
276.4.g.a ✓ 24 23.b odd 2 1 inner
276.4.g.a ✓ 24 69.c even 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(276, [\chi])\).