Properties

Label 24.4.a.a
Level 24
Weight 4
Character orbit 24.a
Self dual Yes
Analytic conductor 1.416
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 24.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.41604584014\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 14q^{5} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 14q^{5} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut -\mathstrut 28q^{11} \) \(\mathstrut -\mathstrut 74q^{13} \) \(\mathstrut +\mathstrut 42q^{15} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 92q^{19} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut +\mathstrut 27q^{27} \) \(\mathstrut -\mathstrut 138q^{29} \) \(\mathstrut +\mathstrut 80q^{31} \) \(\mathstrut -\mathstrut 84q^{33} \) \(\mathstrut -\mathstrut 336q^{35} \) \(\mathstrut +\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 222q^{39} \) \(\mathstrut +\mathstrut 282q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 126q^{45} \) \(\mathstrut +\mathstrut 240q^{47} \) \(\mathstrut +\mathstrut 233q^{49} \) \(\mathstrut +\mathstrut 246q^{51} \) \(\mathstrut -\mathstrut 130q^{53} \) \(\mathstrut -\mathstrut 392q^{55} \) \(\mathstrut +\mathstrut 276q^{57} \) \(\mathstrut +\mathstrut 596q^{59} \) \(\mathstrut -\mathstrut 218q^{61} \) \(\mathstrut -\mathstrut 216q^{63} \) \(\mathstrut -\mathstrut 1036q^{65} \) \(\mathstrut -\mathstrut 436q^{67} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 856q^{71} \) \(\mathstrut -\mathstrut 998q^{73} \) \(\mathstrut +\mathstrut 213q^{75} \) \(\mathstrut +\mathstrut 672q^{77} \) \(\mathstrut -\mathstrut 32q^{79} \) \(\mathstrut +\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 1508q^{83} \) \(\mathstrut +\mathstrut 1148q^{85} \) \(\mathstrut -\mathstrut 414q^{87} \) \(\mathstrut -\mathstrut 246q^{89} \) \(\mathstrut +\mathstrut 1776q^{91} \) \(\mathstrut +\mathstrut 240q^{93} \) \(\mathstrut +\mathstrut 1288q^{95} \) \(\mathstrut +\mathstrut 866q^{97} \) \(\mathstrut -\mathstrut 252q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 3.00000 0 14.0000 0 −24.0000 0 9.00000 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 \(S_{4}^{\mathrm{new}}(\Gamma_0(24))\).