Properties

Label 24.3.h.a
Level 24
Weight 3
Character orbit 24.h
Self dual Yes
Analytic conductor 0.654
Analytic rank 0
Dimension 1
CM disc. -24
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 24.h (of order \(2\) and degree \(1\))

Newform invariants

Self dual: Yes
Analytic conductor: \(0.653952634465\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 20q^{14} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut +\mathstrut 20q^{22} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut -\mathstrut 21q^{25} \) \(\mathstrut +\mathstrut 27q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut +\mathstrut 50q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 38q^{31} \) \(\mathstrut -\mathstrut 32q^{32} \) \(\mathstrut -\mathstrut 30q^{33} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 36q^{36} \) \(\mathstrut -\mathstrut 16q^{40} \) \(\mathstrut +\mathstrut 60q^{42} \) \(\mathstrut -\mathstrut 40q^{44} \) \(\mathstrut +\mathstrut 18q^{45} \) \(\mathstrut +\mathstrut 48q^{48} \) \(\mathstrut +\mathstrut 51q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 54q^{54} \) \(\mathstrut -\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut 80q^{56} \) \(\mathstrut -\mathstrut 100q^{58} \) \(\mathstrut -\mathstrut 10q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut -\mathstrut 76q^{62} \) \(\mathstrut -\mathstrut 90q^{63} \) \(\mathstrut +\mathstrut 64q^{64} \) \(\mathstrut +\mathstrut 60q^{66} \) \(\mathstrut +\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 63q^{75} \) \(\mathstrut +\mathstrut 100q^{77} \) \(\mathstrut -\mathstrut 58q^{79} \) \(\mathstrut +\mathstrut 32q^{80} \) \(\mathstrut +\mathstrut 81q^{81} \) \(\mathstrut +\mathstrut 134q^{83} \) \(\mathstrut -\mathstrut 120q^{84} \) \(\mathstrut +\mathstrut 150q^{87} \) \(\mathstrut +\mathstrut 80q^{88} \) \(\mathstrut -\mathstrut 36q^{90} \) \(\mathstrut +\mathstrut 114q^{93} \) \(\mathstrut -\mathstrut 96q^{96} \) \(\mathstrut -\mathstrut 190q^{97} \) \(\mathstrut -\mathstrut 102q^{98} \) \(\mathstrut -\mathstrut 90q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/24\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(13\) \(17\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5.1
0
−2.00000 3.00000 4.00000 2.00000 −6.00000 −10.0000 −8.00000 9.00000 −4.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char. orbit Parity Mult. Self Twist Proved
1.a Even 1 trivial yes
24.h Odd 1 CM by \(\Q(\sqrt{-6}) \) yes

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{5} \) \(\mathstrut -\mathstrut 2 \) acting on \(S_{3}^{\mathrm{new}}(24, [\chi])\).