Properties

Label 8024.2.a.bb
Level 8024
Weight 2
Character orbit 8024.a
Self dual Yes
Analytic conductor 64.072
Analytic rank 0
Dimension 32
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: \(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \(32q \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut +\mathstrut 40q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(32q \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut +\mathstrut 40q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 32q^{17} \) \(\mathstrut +\mathstrut 14q^{19} \) \(\mathstrut -\mathstrut 7q^{21} \) \(\mathstrut +\mathstrut 7q^{23} \) \(\mathstrut +\mathstrut 38q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut +\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{31} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 21q^{37} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 49q^{41} \) \(\mathstrut -\mathstrut 7q^{43} \) \(\mathstrut +\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut +\mathstrut 37q^{49} \) \(\mathstrut +\mathstrut 12q^{53} \) \(\mathstrut +\mathstrut 15q^{55} \) \(\mathstrut +\mathstrut 45q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut +\mathstrut 5q^{61} \) \(\mathstrut -\mathstrut 12q^{63} \) \(\mathstrut +\mathstrut 39q^{65} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 70q^{73} \) \(\mathstrut -\mathstrut 47q^{75} \) \(\mathstrut -\mathstrut 10q^{77} \) \(\mathstrut -\mathstrut q^{79} \) \(\mathstrut +\mathstrut 84q^{81} \) \(\mathstrut -\mathstrut 17q^{83} \) \(\mathstrut +\mathstrut 8q^{85} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 36q^{91} \) \(\mathstrut +\mathstrut 2q^{93} \) \(\mathstrut -\mathstrut q^{95} \) \(\mathstrut +\mathstrut 58q^{97} \) \(\mathstrut +\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.16628 0 −1.06664 0 −0.836052 0 7.02534 0
1.2 0 −3.01806 0 3.78696 0 −1.07498 0 6.10866 0
1.3 0 −2.97402 0 −3.33527 0 3.60888 0 5.84478 0
1.4 0 −2.96706 0 3.51833 0 3.62712 0 5.80344 0
1.5 0 −2.65698 0 −1.37353 0 −4.51033 0 4.05953 0
1.6 0 −2.35639 0 1.88610 0 −3.68573 0 2.55257 0
1.7 0 −2.29360 0 −3.85032 0 1.95004 0 2.26061 0
1.8 0 −2.23251 0 3.10540 0 −3.44467 0 1.98408 0
1.9 0 −1.67764 0 −0.206110 0 −1.52712 0 −0.185517 0
1.10 0 −1.26190 0 1.28218 0 −0.0440837 0 −1.40761 0
1.11 0 −1.21753 0 0.238125 0 5.25396 0 −1.51763 0
1.12 0 −1.11553 0 −3.13935 0 0.425117 0 −1.75560 0
1.13 0 −0.551342 0 0.616724 0 1.02317 0 −2.69602 0
1.14 0 −0.394982 0 −0.737434 0 −1.31966 0 −2.84399 0
1.15 0 −0.321300 0 3.25819 0 3.32621 0 −2.89677 0
1.16 0 −0.159636 0 −1.22368 0 3.18149 0 −2.97452 0
1.17 0 0.0290013 0 3.75701 0 −1.56335 0 −2.99916 0
1.18 0 0.147881 0 −3.84317 0 −0.153864 0 −2.97813 0
1.19 0 0.792010 0 −0.983575 0 1.99855 0 −2.37272 0
1.20 0 0.804465 0 3.90815 0 3.10524 0 −2.35284 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.32
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8024))\):

\(T_{3}^{32} - \cdots\)
\(T_{5}^{32} - \cdots\)
\(T_{7}^{32} + \cdots\)