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Properties

Label 8024.2.a.z
Level $8024$
Weight $2$
Character orbit 8024.a
Self dual yes
Analytic conductor $64.072$
Analytic rank $1$
Dimension $24$
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: \(1\)
Dimension: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 5 q^{3} - 7 q^{5} - 12 q^{7} + 33 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 5 q^{3} - 7 q^{5} - 12 q^{7} + 33 q^{9} - 15 q^{11} - 17 q^{13} - 7 q^{15} + 24 q^{17} - q^{19} + 10 q^{21} - 21 q^{23} + 19 q^{25} - 26 q^{27} - 18 q^{29} - 23 q^{31} + 10 q^{33} - 5 q^{35} - 29 q^{37} - 44 q^{39} + 14 q^{41} - 23 q^{43} - 24 q^{45} - 17 q^{47} + 46 q^{49} - 5 q^{51} + 7 q^{53} - 33 q^{55} - 2 q^{57} + 24 q^{59} - 9 q^{61} - 52 q^{63} - 15 q^{65} + 2 q^{67} + 2 q^{69} - 51 q^{71} - 18 q^{73} + 7 q^{75} + 14 q^{77} - 36 q^{79} + 12 q^{81} - 39 q^{83} - 7 q^{85} - 5 q^{87} + 46 q^{89} - 52 q^{91} - 20 q^{93} - 52 q^{95} + 50 q^{97} - 53 q^{99}+O(q^{100}) \) 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 −3.34883 0 −3.47894 0 0.106546 0 8.21465 0
1.2 0 −3.33010 0 2.01797 0 −2.90539 0 8.08959 0
1.3 0 −2.97688 0 0.00923108 0 −2.57666 0 5.86179 0
1.4 0 −2.58401 0 1.28987 0 3.31857 0 3.67713 0
1.5 0 −2.20476 0 3.30270 0 −4.05648 0 1.86097 0
1.6 0 −2.15097 0 −2.56894 0 2.78287 0 1.62668 0
1.7 0 −2.04980 0 −1.32805 0 2.42832 0 1.20169 0
1.8 0 −1.96328 0 −2.74825 0 −4.75780 0 0.854459 0
1.9 0 −1.73371 0 2.38550 0 2.01867 0 0.00574433 0
1.10 0 −1.49004 0 0.108881 0 −3.53275 0 −0.779786 0
1.11 0 −0.444555 0 −4.20344 0 −3.82047 0 −2.80237 0
1.12 0 −0.328743 0 −1.06160 0 1.36558 0 −2.89193 0
1.13 0 −0.0391719 0 3.50403 0 −3.34674 0 −2.99847 0
1.14 0 0.121198 0 1.71107 0 4.41457 0 −2.98531 0
1.15 0 0.394976 0 −0.816592 0 −3.20213 0 −2.84399 0
1.16 0 1.18884 0 2.32992 0 −1.08746 0 −1.58666 0
1.17 0 1.54596 0 −2.73839 0 −0.496104 0 −0.610001 0
1.18 0 1.64815 0 −1.50738 0 4.54063 0 −0.283613 0
1.19 0 1.93554 0 0.236703 0 1.77739 0 0.746320 0
1.20 0 1.98886 0 −1.97393 0 3.06713 0 0.955583 0
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
\(2\) \(1\)
\(17\) \(-1\)
\(59\) \(-1\)

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.z ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8024.2.a.z ✓ 24 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8024))\):

\( T_{3}^{24} + 5 T_{3}^{23} - 40 T_{3}^{22} - 223 T_{3}^{21} + 656 T_{3}^{20} + 4274 T_{3}^{19} + \cdots - 704 \) Copy content Toggle raw display
\( T_{5}^{24} + 7 T_{5}^{23} - 45 T_{5}^{22} - 401 T_{5}^{21} + 622 T_{5}^{20} + 9387 T_{5}^{19} + \cdots + 128 \) Copy content Toggle raw display
\( T_{7}^{24} + 12 T_{7}^{23} - 35 T_{7}^{22} - 931 T_{7}^{21} - 1105 T_{7}^{20} + 29101 T_{7}^{19} + \cdots + 27608800 \) Copy content Toggle raw display