Properties

Label 8024.2.a.z
Level 8024
Weight 2
Character orbit 8024.a
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 24
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: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \(24q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 33q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(24q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 33q^{9} \) \(\mathstrut -\mathstrut 15q^{11} \) \(\mathstrut -\mathstrut 17q^{13} \) \(\mathstrut -\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 24q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut -\mathstrut 21q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut -\mathstrut 18q^{29} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut +\mathstrut 10q^{33} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut -\mathstrut 29q^{37} \) \(\mathstrut -\mathstrut 44q^{39} \) \(\mathstrut +\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 23q^{43} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut -\mathstrut 17q^{47} \) \(\mathstrut +\mathstrut 46q^{49} \) \(\mathstrut -\mathstrut 5q^{51} \) \(\mathstrut +\mathstrut 7q^{53} \) \(\mathstrut -\mathstrut 33q^{55} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 9q^{61} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 2q^{67} \) \(\mathstrut +\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 51q^{71} \) \(\mathstrut -\mathstrut 18q^{73} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 14q^{77} \) \(\mathstrut -\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 12q^{81} \) \(\mathstrut -\mathstrut 39q^{83} \) \(\mathstrut -\mathstrut 7q^{85} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 46q^{89} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 20q^{93} \) \(\mathstrut -\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 50q^{97} \) \(\mathstrut -\mathstrut 53q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.34883 0 −3.47894 0 0.106546 0 8.21465 0
1.2 0 −3.33010 0 2.01797 0 −2.90539 0 8.08959 0
1.3 0 −2.97688 0 0.00923108 0 −2.57666 0 5.86179 0
1.4 0 −2.58401 0 1.28987 0 3.31857 0 3.67713 0
1.5 0 −2.20476 0 3.30270 0 −4.05648 0 1.86097 0
1.6 0 −2.15097 0 −2.56894 0 2.78287 0 1.62668 0
1.7 0 −2.04980 0 −1.32805 0 2.42832 0 1.20169 0
1.8 0 −1.96328 0 −2.74825 0 −4.75780 0 0.854459 0
1.9 0 −1.73371 0 2.38550 0 2.01867 0 0.00574433 0
1.10 0 −1.49004 0 0.108881 0 −3.53275 0 −0.779786 0
1.11 0 −0.444555 0 −4.20344 0 −3.82047 0 −2.80237 0
1.12 0 −0.328743 0 −1.06160 0 1.36558 0 −2.89193 0
1.13 0 −0.0391719 0 3.50403 0 −3.34674 0 −2.99847 0
1.14 0 0.121198 0 1.71107 0 4.41457 0 −2.98531 0
1.15 0 0.394976 0 −0.816592 0 −3.20213 0 −2.84399 0
1.16 0 1.18884 0 2.32992 0 −1.08746 0 −1.58666 0
1.17 0 1.54596 0 −2.73839 0 −0.496104 0 −0.610001 0
1.18 0 1.64815 0 −1.50738 0 4.54063 0 −0.283613 0
1.19 0 1.93554 0 0.236703 0 1.77739 0 0.746320 0
1.20 0 1.98886 0 −1.97393 0 3.06713 0 0.955583 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8024))\):

\(T_{3}^{24} + \cdots\)
\(T_{5}^{24} + \cdots\)
\(T_{7}^{24} + \cdots\)