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Properties

Label 1104.3.c.d
Level $1104$
Weight $3$
Character orbit 1104.c
Analytic conductor $30.082$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1104,3,Mod(1057,1104)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1104, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1104.1057");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1104 = 2^{4} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1104.c (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: \(30.0818211854\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 552)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 72 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 72 q^{9} + 40 q^{23} - 152 q^{25} - 32 q^{31} + 304 q^{35} + 48 q^{39} - 80 q^{41} - 88 q^{49} + 64 q^{55} - 144 q^{59} + 48 q^{69} - 128 q^{71} + 192 q^{73} + 96 q^{75} - 144 q^{77} + 216 q^{81} + 384 q^{85} - 288 q^{87} - 240 q^{93} + 304 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1057.1 0 −1.73205 0 − 9.71718i 0 11.7053i 0 3.00000 0
1057.2 0 −1.73205 0 − 8.58023i 0 − 3.24767i 0 3.00000 0
1057.3 0 −1.73205 0 − 4.57967i 0 − 5.63529i 0 3.00000 0
1057.4 0 −1.73205 0 − 3.07987i 0 − 4.14950i 0 3.00000 0
1057.5 0 −1.73205 0 − 1.82488i 0 8.27291i 0 3.00000 0
1057.6 0 −1.73205 0 − 0.152844i 0 − 1.58889i 0 3.00000 0
1057.7 0 −1.73205 0 0.152844i 0 1.58889i 0 3.00000 0
1057.8 0 −1.73205 0 1.82488i 0 − 8.27291i 0 3.00000 0
1057.9 0 −1.73205 0 3.07987i 0 4.14950i 0 3.00000 0
1057.10 0 −1.73205 0 4.57967i 0 5.63529i 0 3.00000 0
1057.11 0 −1.73205 0 8.58023i 0 3.24767i 0 3.00000 0
1057.12 0 −1.73205 0 9.71718i 0 − 11.7053i 0 3.00000 0
1057.13 0 1.73205 0 − 9.16781i 0 6.66748i 0 3.00000 0
1057.14 0 1.73205 0 − 5.79496i 0 − 0.573250i 0 3.00000 0
1057.15 0 1.73205 0 − 5.60385i 0 − 5.74796i 0 3.00000 0
1057.16 0 1.73205 0 − 4.53239i 0 12.8047i 0 3.00000 0
1057.17 0 1.73205 0 − 1.70542i 0 8.76636i 0 3.00000 0
1057.18 0 1.73205 0 − 1.28805i 0 − 6.77241i 0 3.00000 0
1057.19 0 1.73205 0 1.28805i 0 6.77241i 0 3.00000 0
1057.20 0 1.73205 0 1.70542i 0 − 8.76636i 0 3.00000 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1057.24
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1104.3.c.d 24
4.b odd 2 1 552.3.c.a ✓ 24
12.b even 2 1 1656.3.c.c 24
23.b odd 2 1 inner 1104.3.c.d 24
92.b even 2 1 552.3.c.a ✓ 24
276.h odd 2 1 1656.3.c.c 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
552.3.c.a ✓ 24 4.b odd 2 1
552.3.c.a ✓ 24 92.b even 2 1
1104.3.c.d 24 1.a even 1 1 trivial
1104.3.c.d 24 23.b odd 2 1 inner
1656.3.c.c 24 12.b even 2 1
1656.3.c.c 24 276.h odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{24} + 376 T_{5}^{22} + 58444 T_{5}^{20} + 4896576 T_{5}^{18} + 242828900 T_{5}^{16} + \cdots + 945281729536 \) acting on \(S_{3}^{\mathrm{new}}(1104, [\chi])\). Copy content Toggle raw display