Properties

Label 8024.2.a.y
Level 8024
Weight 2
Character orbit 8024.a
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
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: \(23\)
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.

\(\operatorname{Tr}(f)(q) = \) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 23q^{17} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 29q^{23} \) \(\mathstrut +\mathstrut 31q^{25} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 39q^{47} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 35q^{55} \) \(\mathstrut +\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 23q^{59} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut +\mathstrut 33q^{65} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut -\mathstrut 66q^{69} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 81q^{75} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut -\mathstrut 62q^{93} \) \(\mathstrut -\mathstrut 33q^{95} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.24951 0 −3.27317 0 3.90567 0 7.55931 0
1.2 0 −3.11439 0 4.12614 0 1.17263 0 6.69943 0
1.3 0 −2.88993 0 −1.71727 0 −4.47538 0 5.35170 0
1.4 0 −2.64010 0 3.09841 0 −1.88185 0 3.97013 0
1.5 0 −2.07300 0 −3.30236 0 0.766448 0 1.29731 0
1.6 0 −1.74430 0 1.05481 0 1.84260 0 0.0425790 0
1.7 0 −1.61430 0 −1.23431 0 4.85046 0 −0.394052 0
1.8 0 −1.49807 0 −3.21279 0 −1.95127 0 −0.755772 0
1.9 0 −1.40425 0 3.37446 0 −3.92495 0 −1.02809 0
1.10 0 −1.29710 0 −1.23439 0 −2.46133 0 −1.31752 0
1.11 0 −0.823534 0 3.63980 0 3.42292 0 −2.32179 0
1.12 0 −0.725294 0 −2.56147 0 −0.934698 0 −2.47395 0
1.13 0 −0.587444 0 0.0220313 0 3.20930 0 −2.65491 0
1.14 0 0.453475 0 2.43721 0 1.57711 0 −2.79436 0
1.15 0 0.561991 0 −2.34032 0 −3.24647 0 −2.68417 0
1.16 0 1.04245 0 −0.295436 0 1.92039 0 −1.91330 0
1.17 0 1.25653 0 3.93457 0 −3.56420 0 −1.42113 0
1.18 0 1.45598 0 −0.727716 0 2.11595 0 −0.880108 0
1.19 0 2.15021 0 1.53922 0 −0.745521 0 1.62340 0
1.20 0 2.41453 0 0.0537401 0 0.349134 0 2.82994 0
See all 23 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.23
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8024))\):

\(T_{3}^{23} + \cdots\)
\(T_{5}^{23} - \cdots\)
\(T_{7}^{23} + \cdots\)