Properties

Label 24.2.a.a
Level 24
Weight 2
Character orbit 24.a
Self dual Yes
Analytic conductor 0.192
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(0.191640964851\)
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

\(f(q)\) \(=\) \( q - q^{3} - 2q^{5} + q^{9} + O(q^{10}) \) \( q - q^{3} - 2q^{5} + q^{9} + 4q^{11} - 2q^{13} + 2q^{15} + 2q^{17} - 4q^{19} - 8q^{23} - q^{25} - q^{27} + 6q^{29} + 8q^{31} - 4q^{33} + 6q^{37} + 2q^{39} - 6q^{41} + 4q^{43} - 2q^{45} - 7q^{49} - 2q^{51} - 2q^{53} - 8q^{55} + 4q^{57} + 4q^{59} - 2q^{61} + 4q^{65} - 4q^{67} + 8q^{69} + 8q^{71} + 10q^{73} + q^{75} - 8q^{79} + q^{81} - 4q^{83} - 4q^{85} - 6q^{87} - 6q^{89} - 8q^{93} + 8q^{95} + 2q^{97} + 4q^{99} + O(q^{100}) \)

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 −1.00000 0 −2.00000 0 0 0 1.00000 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

There are no other newforms in \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\).