Properties

Label 24.8.a.c
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

\(f(q)\) \(=\) \( q + 27q^{3} + 110q^{5} + 504q^{7} + 729q^{9} + O(q^{10}) \) \( q + 27q^{3} + 110q^{5} + 504q^{7} + 729q^{9} + 3812q^{11} + 9574q^{13} + 2970q^{15} + 26098q^{17} - 38308q^{19} + 13608q^{21} - 71128q^{23} - 66025q^{25} + 19683q^{27} + 74262q^{29} - 275680q^{31} + 102924q^{33} + 55440q^{35} - 266610q^{37} + 258498q^{39} + 684762q^{41} + 245956q^{43} + 80190q^{45} + 478800q^{47} - 569527q^{49} + 704646q^{51} - 569410q^{53} + 419320q^{55} - 1034316q^{57} - 1525324q^{59} - 2640458q^{61} + 367416q^{63} + 1053140q^{65} + 1416236q^{67} - 1920456q^{69} - 3511304q^{71} + 4738618q^{73} - 1782675q^{75} + 1921248q^{77} + 4661488q^{79} + 531441q^{81} - 5729252q^{83} + 2870780q^{85} + 2005074q^{87} + 11993514q^{89} + 4825296q^{91} - 7443360q^{93} - 4213880q^{95} + 7150754q^{97} + 2778948q^{99} + O(q^{100}) \)

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 0 110.000 0 504.000 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 \( T_{5} - 110 \) acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(24))\).