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Properties

Label 5929.2.a.cg
Level $5929$
Weight $2$
Character orbit 5929.a
Self dual yes
Analytic conductor $47.343$
Analytic rank $1$
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] = [5929,2,Mod(1,5929)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5929, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5929.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5929 = 7^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5929.a (trivial)

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: yes
Analytic conductor: \(47.3433033584\)
Analytic rank: \(1\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 539)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 10 q^{2} + 22 q^{4} - 30 q^{8} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 10 q^{2} + 22 q^{4} - 30 q^{8} + 20 q^{9} - 12 q^{15} + 10 q^{16} - 34 q^{18} + 24 q^{25} - 60 q^{29} - 40 q^{30} - 40 q^{32} + 30 q^{36} - 40 q^{37} - 52 q^{39} - 28 q^{43} - 14 q^{46} - 42 q^{50} - 80 q^{51} - 8 q^{53} - 28 q^{57} + 68 q^{58} + 30 q^{64} - 64 q^{65} - 44 q^{71} - 42 q^{72} - 26 q^{74} + 156 q^{78} - 96 q^{79} + 28 q^{81} - 84 q^{85} + 16 q^{86} - 76 q^{92} - 88 q^{93} - 96 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.67292 −1.20049 5.14449 −3.07072 3.20882 0 −8.40495 −1.55882 8.20778
1.2 −2.67292 1.20049 5.14449 3.07072 −3.20882 0 −8.40495 −1.55882 −8.20778
1.3 −2.60683 −2.87106 4.79555 1.91458 7.48435 0 −7.28752 5.24296 −4.99099
1.4 −2.60683 2.87106 4.79555 −1.91458 −7.48435 0 −7.28752 5.24296 4.99099
1.5 −2.02582 −2.82400 2.10395 −2.70214 5.72091 0 −0.210575 4.97497 5.47404
1.6 −2.02582 2.82400 2.10395 2.70214 −5.72091 0 −0.210575 4.97497 −5.47404
1.7 −1.73238 −0.281706 1.00115 4.24073 0.488022 0 1.73039 −2.92064 −7.34658
1.8 −1.73238 0.281706 1.00115 −4.24073 −0.488022 0 1.73039 −2.92064 7.34658
1.9 −1.52671 −0.656135 0.330842 −1.84253 1.00173 0 2.54832 −2.56949 2.81301
1.10 −1.52671 0.656135 0.330842 1.84253 −1.00173 0 2.54832 −2.56949 −2.81301
1.11 −0.899304 −3.26393 −1.19125 1.35208 2.93527 0 2.86991 7.65324 −1.21593
1.12 −0.899304 3.26393 −1.19125 −1.35208 −2.93527 0 2.86991 7.65324 1.21593
1.13 −0.164721 −0.583822 −1.97287 1.89466 0.0961680 0 0.654416 −2.65915 −0.312091
1.14 −0.164721 0.583822 −1.97287 −1.89466 −0.0961680 0 0.654416 −2.65915 0.312091
1.15 0.428861 −2.37249 −1.81608 −0.326257 −1.01747 0 −1.63657 2.62871 −0.139919
1.16 0.428861 2.37249 −1.81608 0.326257 1.01747 0 −1.63657 2.62871 0.139919
1.17 0.980884 −1.97569 −1.03787 1.67171 −1.93792 0 −2.97979 0.903350 1.63975
1.18 0.980884 1.97569 −1.03787 −1.67171 1.93792 0 −2.97979 0.903350 −1.63975
1.19 1.13999 −0.989432 −0.700421 −2.74105 −1.12794 0 −3.07846 −2.02102 −3.12477
1.20 1.13999 0.989432 −0.700421 2.74105 1.12794 0 −3.07846 −2.02102 3.12477
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(7\) \(1\)
\(11\) \(1\)

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5929.2.a.cg 24
7.b odd 2 1 inner 5929.2.a.cg 24
11.b odd 2 1 5929.2.a.ch 24
11.c even 5 2 539.2.f.i ✓ 48
77.b even 2 1 5929.2.a.ch 24
77.j odd 10 2 539.2.f.i ✓ 48
77.m even 15 4 539.2.q.i 96
77.p odd 30 4 539.2.q.i 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
539.2.f.i ✓ 48 11.c even 5 2
539.2.f.i ✓ 48 77.j odd 10 2
539.2.q.i 96 77.m even 15 4
539.2.q.i 96 77.p odd 30 4
5929.2.a.cg 24 1.a even 1 1 trivial
5929.2.a.cg 24 7.b odd 2 1 inner
5929.2.a.ch 24 11.b odd 2 1
5929.2.a.ch 24 77.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5929))\):

\( T_{2}^{12} + 5 T_{2}^{11} - 5 T_{2}^{10} - 55 T_{2}^{9} - 23 T_{2}^{8} + 208 T_{2}^{7} + 169 T_{2}^{6} + \cdots - 11 \) Copy content Toggle raw display
\( T_{3}^{24} - 46 T_{3}^{22} + 898 T_{3}^{20} - 9738 T_{3}^{18} + 64527 T_{3}^{16} - 271184 T_{3}^{14} + \cdots + 1936 \) Copy content Toggle raw display
\( T_{5}^{24} - 72 T_{5}^{22} + 2212 T_{5}^{20} - 38254 T_{5}^{18} + 413566 T_{5}^{16} - 2932900 T_{5}^{14} + \cdots + 2062096 \) Copy content Toggle raw display