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

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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: \(1\)
Dimension: \(22\)
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.

\(\operatorname{Tr}(f)(q) = \) \(22q \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(22q \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut -\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 7q^{15} \) \(\mathstrut -\mathstrut 22q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut -\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 14q^{23} \) \(\mathstrut +\mathstrut 3q^{25} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 15q^{31} \) \(\mathstrut -\mathstrut 52q^{33} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 9q^{37} \) \(\mathstrut -\mathstrut 52q^{41} \) \(\mathstrut -\mathstrut 7q^{43} \) \(\mathstrut -\mathstrut 30q^{45} \) \(\mathstrut -\mathstrut 7q^{47} \) \(\mathstrut -\mathstrut 6q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 39q^{55} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut +\mathstrut 22q^{59} \) \(\mathstrut -\mathstrut 42q^{61} \) \(\mathstrut -\mathstrut 35q^{65} \) \(\mathstrut -\mathstrut 28q^{67} \) \(\mathstrut -\mathstrut 10q^{69} \) \(\mathstrut +\mathstrut 23q^{71} \) \(\mathstrut -\mathstrut 33q^{73} \) \(\mathstrut -\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 28q^{77} \) \(\mathstrut -\mathstrut 30q^{79} \) \(\mathstrut -\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 11q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 27q^{87} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut -\mathstrut 28q^{93} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 3q^{97} \) \(\mathstrut -\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.05613 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:

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

\(T_{3}^{22} + \cdots\)
\(T_{5}^{22} - \cdots\)
\(T_{7}^{22} - \cdots\)