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Properties

Label 8024.2.a.ba
Level $8024$
Weight $2$
Character orbit 8024.a
Self dual yes
Analytic conductor $64.072$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8024,2,Mod(1,8024)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8024, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("8024.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8024.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: \(64.0719625819\)
Analytic rank: \(0\)
Dimension: \(30\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 30 q + 4 q^{3} + 2 q^{5} + 3 q^{7} + 34 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 30 q + 4 q^{3} + 2 q^{5} + 3 q^{7} + 34 q^{9} + 3 q^{11} + 9 q^{13} + 14 q^{15} - 30 q^{17} + 24 q^{19} + 7 q^{21} + 9 q^{23} + 40 q^{25} + 19 q^{27} + 9 q^{29} + 11 q^{31} - 14 q^{33} + 30 q^{35} - 13 q^{37} + 16 q^{39} - 13 q^{41} + 23 q^{43} + 12 q^{45} + 43 q^{47} + 35 q^{49} - 4 q^{51} - 4 q^{53} + 43 q^{55} + 3 q^{57} + 30 q^{59} + 43 q^{61} + 38 q^{63} + 3 q^{65} + 50 q^{67} + 34 q^{69} + 3 q^{71} - 16 q^{73} + 21 q^{75} + 18 q^{77} + 45 q^{79} + 6 q^{81} + 63 q^{83} - 2 q^{85} + 42 q^{87} + 6 q^{89} + 22 q^{91} - 2 q^{93} + 19 q^{95} - 28 q^{97} + 51 q^{99}+O(q^{100}) \) 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 0 −3.16175 0 −1.04062 0 −0.359718 0 6.99664 0
1.2 0 −2.78964 0 3.12966 0 4.93262 0 4.78208 0
1.3 0 −2.64071 0 −0.794586 0 0.767339 0 3.97338 0
1.4 0 −2.51295 0 1.54397 0 0.259224 0 3.31493 0
1.5 0 −2.45601 0 −4.36019 0 −1.77500 0 3.03197 0
1.6 0 −2.34066 0 −1.86440 0 −5.20859 0 2.47869 0
1.7 0 −1.93944 0 −3.21458 0 1.58526 0 0.761421 0
1.8 0 −1.91871 0 0.891187 0 4.37465 0 0.681439 0
1.9 0 −1.35103 0 3.55112 0 −1.74593 0 −1.17470 0
1.10 0 −1.33836 0 2.46602 0 0.387813 0 −1.20880 0
1.11 0 −1.15878 0 0.502804 0 −3.23776 0 −1.65724 0
1.12 0 −0.797176 0 −2.84462 0 −0.0983465 0 −2.36451 0
1.13 0 −0.566412 0 0.586437 0 −1.33450 0 −2.67918 0
1.14 0 0.234948 0 4.33432 0 1.77709 0 −2.94480 0
1.15 0 0.278925 0 −0.331672 0 −3.80864 0 −2.92220 0
1.16 0 0.477393 0 1.25877 0 1.96440 0 −2.77210 0
1.17 0 0.540046 0 1.83529 0 −2.95966 0 −2.70835 0
1.18 0 0.597652 0 −3.19982 0 4.21450 0 −2.64281 0
1.19 0 0.974333 0 −2.75294 0 −1.75498 0 −2.05067 0
1.20 0 0.991965 0 2.29317 0 3.07900 0 −2.01601 0
See all 30 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.30
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(17\) \(1\)
\(59\) \(-1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 8024.2.a.ba ✓ 30
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8024.2.a.ba ✓ 30 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8024))\):

\( T_{3}^{30} - 4 T_{3}^{29} - 54 T_{3}^{28} + 223 T_{3}^{27} + 1281 T_{3}^{26} - 5509 T_{3}^{25} + \cdots - 77440 \) Copy content Toggle raw display
\( T_{5}^{30} - 2 T_{5}^{29} - 93 T_{5}^{28} + 182 T_{5}^{27} + 3833 T_{5}^{26} - 7351 T_{5}^{25} + \cdots + 74911904 \) Copy content Toggle raw display
\( T_{7}^{30} - 3 T_{7}^{29} - 118 T_{7}^{28} + 313 T_{7}^{27} + 6085 T_{7}^{26} - 13652 T_{7}^{25} + \cdots + 1859584 \) Copy content Toggle raw display