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

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

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