Properties

Label 24.6.a.b
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

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 94q^{5} \) \(\mathstrut +\mathstrut 144q^{7} \) \(\mathstrut +\mathstrut 81q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 94q^{5} \) \(\mathstrut +\mathstrut 144q^{7} \) \(\mathstrut +\mathstrut 81q^{9} \) \(\mathstrut -\mathstrut 380q^{11} \) \(\mathstrut +\mathstrut 814q^{13} \) \(\mathstrut -\mathstrut 846q^{15} \) \(\mathstrut -\mathstrut 862q^{17} \) \(\mathstrut -\mathstrut 1156q^{19} \) \(\mathstrut -\mathstrut 1296q^{21} \) \(\mathstrut -\mathstrut 488q^{23} \) \(\mathstrut +\mathstrut 5711q^{25} \) \(\mathstrut -\mathstrut 729q^{27} \) \(\mathstrut -\mathstrut 5466q^{29} \) \(\mathstrut +\mathstrut 9560q^{31} \) \(\mathstrut +\mathstrut 3420q^{33} \) \(\mathstrut +\mathstrut 13536q^{35} \) \(\mathstrut -\mathstrut 10506q^{37} \) \(\mathstrut -\mathstrut 7326q^{39} \) \(\mathstrut -\mathstrut 5190q^{41} \) \(\mathstrut -\mathstrut 17084q^{43} \) \(\mathstrut +\mathstrut 7614q^{45} \) \(\mathstrut +\mathstrut 3168q^{47} \) \(\mathstrut +\mathstrut 3929q^{49} \) \(\mathstrut +\mathstrut 7758q^{51} \) \(\mathstrut -\mathstrut 24770q^{53} \) \(\mathstrut -\mathstrut 35720q^{55} \) \(\mathstrut +\mathstrut 10404q^{57} \) \(\mathstrut +\mathstrut 17380q^{59} \) \(\mathstrut +\mathstrut 4366q^{61} \) \(\mathstrut +\mathstrut 11664q^{63} \) \(\mathstrut +\mathstrut 76516q^{65} \) \(\mathstrut -\mathstrut 5284q^{67} \) \(\mathstrut +\mathstrut 4392q^{69} \) \(\mathstrut +\mathstrut 8360q^{71} \) \(\mathstrut +\mathstrut 39466q^{73} \) \(\mathstrut -\mathstrut 51399q^{75} \) \(\mathstrut -\mathstrut 54720q^{77} \) \(\mathstrut +\mathstrut 42376q^{79} \) \(\mathstrut +\mathstrut 6561q^{81} \) \(\mathstrut -\mathstrut 61828q^{83} \) \(\mathstrut -\mathstrut 81028q^{85} \) \(\mathstrut +\mathstrut 49194q^{87} \) \(\mathstrut -\mathstrut 63078q^{89} \) \(\mathstrut +\mathstrut 117216q^{91} \) \(\mathstrut -\mathstrut 86040q^{93} \) \(\mathstrut -\mathstrut 108664q^{95} \) \(\mathstrut -\mathstrut 16318q^{97} \) \(\mathstrut -\mathstrut 30780q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 94.0000 0 144.000 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 \(T_{5} \) \(\mathstrut -\mathstrut 94 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(24))\).