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

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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: \(30\)
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.

\(\operatorname{Tr}(f)(q) = \) \(30q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut +\mathstrut 34q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(30q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut +\mathstrut 34q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut +\mathstrut 14q^{15} \) \(\mathstrut -\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 7q^{21} \) \(\mathstrut +\mathstrut 9q^{23} \) \(\mathstrut +\mathstrut 40q^{25} \) \(\mathstrut +\mathstrut 19q^{27} \) \(\mathstrut +\mathstrut 9q^{29} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut -\mathstrut 14q^{33} \) \(\mathstrut +\mathstrut 30q^{35} \) \(\mathstrut -\mathstrut 13q^{37} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut -\mathstrut 13q^{41} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 12q^{45} \) \(\mathstrut +\mathstrut 43q^{47} \) \(\mathstrut +\mathstrut 35q^{49} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 4q^{53} \) \(\mathstrut +\mathstrut 43q^{55} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut +\mathstrut 30q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 38q^{63} \) \(\mathstrut +\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 50q^{67} \) \(\mathstrut +\mathstrut 34q^{69} \) \(\mathstrut +\mathstrut 3q^{71} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 21q^{75} \) \(\mathstrut +\mathstrut 18q^{77} \) \(\mathstrut +\mathstrut 45q^{79} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut +\mathstrut 63q^{83} \) \(\mathstrut -\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 42q^{87} \) \(\mathstrut +\mathstrut 6q^{89} \) \(\mathstrut +\mathstrut 22q^{91} \) \(\mathstrut -\mathstrut 2q^{93} \) \(\mathstrut +\mathstrut 19q^{95} \) \(\mathstrut -\mathstrut 28q^{97} \) \(\mathstrut +\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.16175 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:

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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8024))\):

\(T_{3}^{30} - \cdots\)
\(T_{5}^{30} - \cdots\)
\(T_{7}^{30} - \cdots\)