Properties

Label 24.8.a.a
Level 24
Weight 8
Character orbit 24.a
Self dual Yes
Analytic conductor 7.497
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 24.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(7.49724061162\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut -\mathstrut 26q^{5} \) \(\mathstrut +\mathstrut 1056q^{7} \) \(\mathstrut +\mathstrut 729q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut -\mathstrut 26q^{5} \) \(\mathstrut +\mathstrut 1056q^{7} \) \(\mathstrut +\mathstrut 729q^{9} \) \(\mathstrut +\mathstrut 6412q^{11} \) \(\mathstrut +\mathstrut 5206q^{13} \) \(\mathstrut +\mathstrut 702q^{15} \) \(\mathstrut -\mathstrut 6238q^{17} \) \(\mathstrut +\mathstrut 41492q^{19} \) \(\mathstrut -\mathstrut 28512q^{21} \) \(\mathstrut -\mathstrut 29432q^{23} \) \(\mathstrut -\mathstrut 77449q^{25} \) \(\mathstrut -\mathstrut 19683q^{27} \) \(\mathstrut -\mathstrut 210498q^{29} \) \(\mathstrut +\mathstrut 185240q^{31} \) \(\mathstrut -\mathstrut 173124q^{33} \) \(\mathstrut -\mathstrut 27456q^{35} \) \(\mathstrut +\mathstrut 507630q^{37} \) \(\mathstrut -\mathstrut 140562q^{39} \) \(\mathstrut +\mathstrut 360042q^{41} \) \(\mathstrut +\mathstrut 620044q^{43} \) \(\mathstrut -\mathstrut 18954q^{45} \) \(\mathstrut -\mathstrut 847680q^{47} \) \(\mathstrut +\mathstrut 291593q^{49} \) \(\mathstrut +\mathstrut 168426q^{51} \) \(\mathstrut +\mathstrut 1423750q^{53} \) \(\mathstrut -\mathstrut 166712q^{55} \) \(\mathstrut -\mathstrut 1120284q^{57} \) \(\mathstrut -\mathstrut 2548724q^{59} \) \(\mathstrut -\mathstrut 706058q^{61} \) \(\mathstrut +\mathstrut 769824q^{63} \) \(\mathstrut -\mathstrut 135356q^{65} \) \(\mathstrut -\mathstrut 2418796q^{67} \) \(\mathstrut +\mathstrut 794664q^{69} \) \(\mathstrut +\mathstrut 265976q^{71} \) \(\mathstrut -\mathstrut 5791238q^{73} \) \(\mathstrut +\mathstrut 2091123q^{75} \) \(\mathstrut +\mathstrut 6771072q^{77} \) \(\mathstrut +\mathstrut 2955688q^{79} \) \(\mathstrut +\mathstrut 531441q^{81} \) \(\mathstrut +\mathstrut 3462932q^{83} \) \(\mathstrut +\mathstrut 162188q^{85} \) \(\mathstrut +\mathstrut 5683446q^{87} \) \(\mathstrut -\mathstrut 2211126q^{89} \) \(\mathstrut +\mathstrut 5497536q^{91} \) \(\mathstrut -\mathstrut 5001480q^{93} \) \(\mathstrut -\mathstrut 1078792q^{95} \) \(\mathstrut -\mathstrut 15594814q^{97} \) \(\mathstrut +\mathstrut 4674348q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
0 −27.0000 0 −26.0000 0 1056.00 0 729.000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{5} \) \(\mathstrut +\mathstrut 26 \) acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(24))\).