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Properties

Label 8024.2.a.x
Level $8024$
Weight $2$
Character orbit 8024.a
Self dual yes
Analytic conductor $64.072$
Analytic rank $1$
Dimension $22$
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: \(22\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 22 q - 3 q^{3} + 3 q^{5} + 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 22 q - 3 q^{3} + 3 q^{5} + 13 q^{9} + 2 q^{11} - 9 q^{13} - 7 q^{15} - 22 q^{17} - 10 q^{19} - 10 q^{21} + 14 q^{23} + 3 q^{25} + 6 q^{29} - 15 q^{31} - 52 q^{33} - 7 q^{35} + 9 q^{37} - 52 q^{41} - 7 q^{43} - 30 q^{45} - 7 q^{47} - 6 q^{49} + 3 q^{51} - 18 q^{53} - 39 q^{55} - 2 q^{57} + 22 q^{59} - 42 q^{61} - 35 q^{65} - 28 q^{67} - 10 q^{69} + 23 q^{71} - 33 q^{73} - 3 q^{75} - 28 q^{77} - 30 q^{79} - 2 q^{81} + 11 q^{83} - 3 q^{85} + 27 q^{87} - 34 q^{89} - 18 q^{91} - 28 q^{93} - 10 q^{95} - 3 q^{97} - 28 q^{99}+O(q^{100}) \) 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 −3.05613 0 −1.88060 0 −1.70270 0 6.33993 0
1.2 0 −2.56466 0 −3.26922 0 2.64610 0 3.57750 0
1.3 0 −2.54005 0 2.36838 0 1.43029 0 3.45187 0
1.4 0 −2.48825 0 −0.882528 0 0.896015 0 3.19137 0
1.5 0 −2.46281 0 3.32357 0 0.836555 0 3.06541 0
1.6 0 −2.02290 0 1.12353 0 −1.44909 0 1.09211 0
1.7 0 −1.63019 0 0.886839 0 −4.44237 0 −0.342474 0
1.8 0 −1.20210 0 1.10558 0 3.71217 0 −1.55495 0
1.9 0 −0.687639 0 −1.07935 0 2.48918 0 −2.52715 0
1.10 0 −0.484590 0 2.40120 0 −0.883019 0 −2.76517 0
1.11 0 −0.0474813 0 2.55871 0 −1.15477 0 −2.99775 0
1.12 0 0.159171 0 −4.24792 0 −1.24523 0 −2.97466 0
1.13 0 0.283630 0 −1.81468 0 −4.62526 0 −2.91955 0
1.14 0 0.325143 0 −1.77729 0 4.59153 0 −2.89428 0
1.15 0 0.535004 0 2.05543 0 0.811137 0 −2.71377 0
1.16 0 1.27679 0 2.13098 0 3.12134 0 −1.36980 0
1.17 0 1.39463 0 4.34845 0 −1.84282 0 −1.05500 0
1.18 0 1.49900 0 −0.909441 0 1.38706 0 −0.753011 0
1.19 0 2.29019 0 0.921405 0 −4.02395 0 2.24495 0
1.20 0 2.44950 0 −0.409784 0 −2.49662 0 3.00004 0
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.22
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.x ✓ 22
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8024.2.a.x ✓ 22 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8024))\):

\( T_{3}^{22} + 3 T_{3}^{21} - 35 T_{3}^{20} - 108 T_{3}^{19} + 496 T_{3}^{18} + 1583 T_{3}^{17} - 3686 T_{3}^{16} + \cdots - 8 \) Copy content Toggle raw display
\( T_{5}^{22} - 3 T_{5}^{21} - 52 T_{5}^{20} + 158 T_{5}^{19} + 1065 T_{5}^{18} - 3304 T_{5}^{17} + \cdots - 70610 \) Copy content Toggle raw display
\( T_{7}^{22} - 74 T_{7}^{20} + 15 T_{7}^{19} + 2222 T_{7}^{18} - 790 T_{7}^{17} - 35244 T_{7}^{16} + \cdots - 1177210 \) Copy content Toggle raw display