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

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

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 \( T_{5} + 26 \) acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(24))\).