Properties

Label 24.6.a.c
Level 24
Weight 6
Character orbit 24.a
Self dual Yes
Analytic conductor 3.849
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 24.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(3.84921167551\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 120q^{7} \) \(\mathstrut +\mathstrut 81q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 120q^{7} \) \(\mathstrut +\mathstrut 81q^{9} \) \(\mathstrut +\mathstrut 524q^{11} \) \(\mathstrut -\mathstrut 962q^{13} \) \(\mathstrut +\mathstrut 342q^{15} \) \(\mathstrut -\mathstrut 1358q^{17} \) \(\mathstrut -\mathstrut 2284q^{19} \) \(\mathstrut +\mathstrut 1080q^{21} \) \(\mathstrut +\mathstrut 2552q^{23} \) \(\mathstrut -\mathstrut 1681q^{25} \) \(\mathstrut +\mathstrut 729q^{27} \) \(\mathstrut +\mathstrut 3966q^{29} \) \(\mathstrut -\mathstrut 2992q^{31} \) \(\mathstrut +\mathstrut 4716q^{33} \) \(\mathstrut +\mathstrut 4560q^{35} \) \(\mathstrut +\mathstrut 13206q^{37} \) \(\mathstrut -\mathstrut 8658q^{39} \) \(\mathstrut -\mathstrut 15126q^{41} \) \(\mathstrut -\mathstrut 7316q^{43} \) \(\mathstrut +\mathstrut 3078q^{45} \) \(\mathstrut -\mathstrut 6960q^{47} \) \(\mathstrut -\mathstrut 2407q^{49} \) \(\mathstrut -\mathstrut 12222q^{51} \) \(\mathstrut -\mathstrut 17482q^{53} \) \(\mathstrut +\mathstrut 19912q^{55} \) \(\mathstrut -\mathstrut 20556q^{57} \) \(\mathstrut +\mathstrut 33884q^{59} \) \(\mathstrut +\mathstrut 39118q^{61} \) \(\mathstrut +\mathstrut 9720q^{63} \) \(\mathstrut -\mathstrut 36556q^{65} \) \(\mathstrut +\mathstrut 32996q^{67} \) \(\mathstrut +\mathstrut 22968q^{69} \) \(\mathstrut +\mathstrut 14248q^{71} \) \(\mathstrut -\mathstrut 35990q^{73} \) \(\mathstrut -\mathstrut 15129q^{75} \) \(\mathstrut +\mathstrut 62880q^{77} \) \(\mathstrut -\mathstrut 29888q^{79} \) \(\mathstrut +\mathstrut 6561q^{81} \) \(\mathstrut -\mathstrut 51884q^{83} \) \(\mathstrut -\mathstrut 51604q^{85} \) \(\mathstrut +\mathstrut 35694q^{87} \) \(\mathstrut +\mathstrut 30714q^{89} \) \(\mathstrut -\mathstrut 115440q^{91} \) \(\mathstrut -\mathstrut 26928q^{93} \) \(\mathstrut -\mathstrut 86792q^{95} \) \(\mathstrut -\mathstrut 48478q^{97} \) \(\mathstrut +\mathstrut 42444q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 9.00000 0 38.0000 0 120.000 0 81.0000 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 \(T_{5} \) \(\mathstrut -\mathstrut 38 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(24))\).