Properties

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

Related objects

Downloads

Learn more about

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: \(1\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 34q^{5} \) \(\mathstrut -\mathstrut 240q^{7} \) \(\mathstrut +\mathstrut 81q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 34q^{5} \) \(\mathstrut -\mathstrut 240q^{7} \) \(\mathstrut +\mathstrut 81q^{9} \) \(\mathstrut -\mathstrut 124q^{11} \) \(\mathstrut +\mathstrut 46q^{13} \) \(\mathstrut +\mathstrut 306q^{15} \) \(\mathstrut +\mathstrut 1954q^{17} \) \(\mathstrut -\mathstrut 1924q^{19} \) \(\mathstrut +\mathstrut 2160q^{21} \) \(\mathstrut +\mathstrut 2840q^{23} \) \(\mathstrut -\mathstrut 1969q^{25} \) \(\mathstrut -\mathstrut 729q^{27} \) \(\mathstrut -\mathstrut 8922q^{29} \) \(\mathstrut -\mathstrut 4648q^{31} \) \(\mathstrut +\mathstrut 1116q^{33} \) \(\mathstrut +\mathstrut 8160q^{35} \) \(\mathstrut -\mathstrut 4362q^{37} \) \(\mathstrut -\mathstrut 414q^{39} \) \(\mathstrut -\mathstrut 2886q^{41} \) \(\mathstrut +\mathstrut 11332q^{43} \) \(\mathstrut -\mathstrut 2754q^{45} \) \(\mathstrut +\mathstrut 7008q^{47} \) \(\mathstrut +\mathstrut 40793q^{49} \) \(\mathstrut -\mathstrut 17586q^{51} \) \(\mathstrut -\mathstrut 22594q^{53} \) \(\mathstrut +\mathstrut 4216q^{55} \) \(\mathstrut +\mathstrut 17316q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 6386q^{61} \) \(\mathstrut -\mathstrut 19440q^{63} \) \(\mathstrut -\mathstrut 1564q^{65} \) \(\mathstrut -\mathstrut 39076q^{67} \) \(\mathstrut -\mathstrut 25560q^{69} \) \(\mathstrut -\mathstrut 54872q^{71} \) \(\mathstrut +\mathstrut 21034q^{73} \) \(\mathstrut +\mathstrut 17721q^{75} \) \(\mathstrut +\mathstrut 29760q^{77} \) \(\mathstrut +\mathstrut 26632q^{79} \) \(\mathstrut +\mathstrut 6561q^{81} \) \(\mathstrut +\mathstrut 56188q^{83} \) \(\mathstrut -\mathstrut 66436q^{85} \) \(\mathstrut +\mathstrut 80298q^{87} \) \(\mathstrut +\mathstrut 64410q^{89} \) \(\mathstrut -\mathstrut 11040q^{91} \) \(\mathstrut +\mathstrut 41832q^{93} \) \(\mathstrut +\mathstrut 65416q^{95} \) \(\mathstrut -\mathstrut 116158q^{97} \) \(\mathstrut -\mathstrut 10044q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −34.0000 0 −240.000 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 \(T_{5} \) \(\mathstrut +\mathstrut 34 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(24))\).