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

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Newspace parameters

Level: \( N \) = \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0719625819\)
Analytic rank: \(0\)
Dimension: \(33\)
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.

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

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.

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:

Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

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

Hecke kernels

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

\(T_{3}^{33} + \cdots\)
\(T_{5}^{33} - \cdots\)
\(T_{7}^{33} - \cdots\)