Properties

Label 8024.2.a.bc
Level $8024$
Weight $2$
Character orbit 8024.a
Self dual yes
Analytic conductor $64.072$
Analytic rank $0$
Dimension $33$
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: \(33\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 33 q - 3 q^{3} + 3 q^{5} + 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 33 q - 3 q^{3} + 3 q^{5} + 48 q^{9} - 7 q^{11} + 9 q^{13} - 7 q^{15} - 33 q^{17} + 5 q^{19} + 14 q^{21} - 19 q^{23} + 52 q^{25} - 24 q^{27} + 14 q^{29} + 19 q^{31} + 34 q^{33} + 15 q^{35} + 13 q^{37} + 26 q^{39} + 32 q^{41} + 11 q^{43} - 27 q^{47} + 93 q^{49} + 3 q^{51} - 7 q^{53} + 31 q^{55} + 6 q^{57} - 33 q^{59} + 33 q^{61} + 10 q^{63} + 21 q^{65} - 10 q^{67} + 78 q^{69} - 29 q^{71} + 30 q^{73} + 31 q^{75} + 6 q^{77} + 66 q^{79} + 97 q^{81} - 9 q^{83} - 3 q^{85} - 27 q^{87} + 68 q^{89} + 28 q^{91} + 34 q^{93} + 8 q^{95} + 62 q^{97} + 15 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 −3.44977 0 2.91669 0 −3.05603 0 8.90091 0
1.2 0 −3.36646 0 0.242538 0 4.57037 0 8.33308 0
1.3 0 −3.33387 0 −3.73347 0 −3.52781 0 8.11466 0
1.4 0 −2.83790 0 2.04357 0 3.25946 0 5.05368 0
1.5 0 −2.77346 0 1.76876 0 −4.75466 0 4.69208 0
1.6 0 −2.56116 0 0.330730 0 −0.779452 0 3.55957 0
1.7 0 −2.22636 0 −2.51166 0 −2.56246 0 1.95667 0
1.8 0 −2.18303 0 −1.35778 0 2.12244 0 1.76561 0
1.9 0 −2.08632 0 −3.87621 0 3.88634 0 1.35275 0
1.10 0 −1.52586 0 4.15650 0 0.772198 0 −0.671760 0
1.11 0 −1.48206 0 0.847914 0 −1.54807 0 −0.803509 0
1.12 0 −1.13464 0 3.41042 0 3.81192 0 −1.71258 0
1.13 0 −0.973545 0 −2.57461 0 0.184041 0 −2.05221 0
1.14 0 −0.882440 0 0.934682 0 3.89754 0 −2.22130 0
1.15 0 −0.772486 0 2.52530 0 −1.43717 0 −2.40327 0
1.16 0 −0.481497 0 −1.68499 0 −3.55584 0 −2.76816 0
1.17 0 0.0609456 0 3.92947 0 −4.97459 0 −2.99629 0
1.18 0 0.270435 0 −0.155002 0 −4.46551 0 −2.92686 0
1.19 0 0.504210 0 1.10428 0 −0.448564 0 −2.74577 0
1.20 0 0.510308 0 −0.733675 0 1.56284 0 −2.73959 0
See all 33 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.33
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.bc 33
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8024.2.a.bc 33 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8024))\):

\( T_{3}^{33} + 3 T_{3}^{32} - 69 T_{3}^{31} - 202 T_{3}^{30} + 2135 T_{3}^{29} + 6084 T_{3}^{28} - 39151 T_{3}^{27} - 108337 T_{3}^{26} + 473735 T_{3}^{25} + 1270129 T_{3}^{24} - 3985452 T_{3}^{23} - 10332869 T_{3}^{22} + \cdots - 148736 \) Copy content Toggle raw display
\( T_{5}^{33} - 3 T_{5}^{32} - 104 T_{5}^{31} + 316 T_{5}^{30} + 4767 T_{5}^{29} - 14780 T_{5}^{28} - 126644 T_{5}^{27} + 404789 T_{5}^{26} + 2156337 T_{5}^{25} - 7209643 T_{5}^{24} - 24538656 T_{5}^{23} + \cdots + 44679680 \) Copy content Toggle raw display
\( T_{7}^{33} - 162 T_{7}^{31} + T_{7}^{30} + 11770 T_{7}^{29} - 200 T_{7}^{28} - 507070 T_{7}^{27} + 16312 T_{7}^{26} + 14430070 T_{7}^{25} - 746624 T_{7}^{24} - 286000513 T_{7}^{23} + 21718475 T_{7}^{22} + \cdots - 87286906880 \) Copy content Toggle raw display