Properties

Label 24.8.a.b
Level 24
Weight 8
Character orbit 24.a
Self dual Yes
Analytic conductor 7.497
Analytic rank 1
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: \(1\)
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

\(f(q)\) \(=\) \( q + 27q^{3} - 530q^{5} + 120q^{7} + 729q^{9} + O(q^{10}) \) \( q + 27q^{3} - 530q^{5} + 120q^{7} + 729q^{9} - 7196q^{11} - 9626q^{13} - 14310q^{15} + 18674q^{17} + 7004q^{19} + 3240q^{21} - 63704q^{23} + 202775q^{25} + 19683q^{27} + 29334q^{29} + 87968q^{31} - 194292q^{33} - 63600q^{35} + 227982q^{37} - 259902q^{39} - 160806q^{41} + 136132q^{43} - 386370q^{45} - 1206960q^{47} - 809143q^{49} + 504198q^{51} - 398786q^{53} + 3813880q^{55} + 189108q^{57} + 1152436q^{59} - 2070602q^{61} + 87480q^{63} + 5101780q^{65} - 4073428q^{67} - 1720008q^{69} - 383752q^{71} + 3006010q^{73} + 5474925q^{75} - 863520q^{77} - 4948112q^{79} + 531441q^{81} - 9163492q^{83} - 9897220q^{85} + 792018q^{87} + 7304106q^{89} - 1155120q^{91} + 2375136q^{93} - 3712120q^{95} - 690526q^{97} - 5245884q^{99} + O(q^{100}) \)

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 −530.000 0 120.000 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 \( T_{5} + 530 \) acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(24))\).