Properties

Label 8.4.a.a
Level 8
Weight 4
Character orbit 8.a
Self dual Yes
Analytic conductor 0.472
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 8.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.472015280046\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 11q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 11q^{9} \) \(\mathstrut -\mathstrut 44q^{11} \) \(\mathstrut +\mathstrut 22q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 50q^{17} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut -\mathstrut 96q^{21} \) \(\mathstrut -\mathstrut 56q^{23} \) \(\mathstrut -\mathstrut 121q^{25} \) \(\mathstrut +\mathstrut 152q^{27} \) \(\mathstrut +\mathstrut 198q^{29} \) \(\mathstrut -\mathstrut 160q^{31} \) \(\mathstrut +\mathstrut 176q^{33} \) \(\mathstrut -\mathstrut 48q^{35} \) \(\mathstrut -\mathstrut 162q^{37} \) \(\mathstrut -\mathstrut 88q^{39} \) \(\mathstrut -\mathstrut 198q^{41} \) \(\mathstrut +\mathstrut 52q^{43} \) \(\mathstrut +\mathstrut 22q^{45} \) \(\mathstrut +\mathstrut 528q^{47} \) \(\mathstrut +\mathstrut 233q^{49} \) \(\mathstrut -\mathstrut 200q^{51} \) \(\mathstrut -\mathstrut 242q^{53} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut -\mathstrut 176q^{57} \) \(\mathstrut -\mathstrut 668q^{59} \) \(\mathstrut +\mathstrut 550q^{61} \) \(\mathstrut -\mathstrut 264q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut +\mathstrut 188q^{67} \) \(\mathstrut +\mathstrut 224q^{69} \) \(\mathstrut +\mathstrut 728q^{71} \) \(\mathstrut +\mathstrut 154q^{73} \) \(\mathstrut +\mathstrut 484q^{75} \) \(\mathstrut -\mathstrut 1056q^{77} \) \(\mathstrut -\mathstrut 656q^{79} \) \(\mathstrut -\mathstrut 311q^{81} \) \(\mathstrut +\mathstrut 236q^{83} \) \(\mathstrut -\mathstrut 100q^{85} \) \(\mathstrut -\mathstrut 792q^{87} \) \(\mathstrut +\mathstrut 714q^{89} \) \(\mathstrut +\mathstrut 528q^{91} \) \(\mathstrut +\mathstrut 640q^{93} \) \(\mathstrut -\mathstrut 88q^{95} \) \(\mathstrut -\mathstrut 478q^{97} \) \(\mathstrut +\mathstrut 484q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −4.00000 0 −2.00000 0 24.0000 0 −11.0000 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
\(2\) \(1\)

Hecke kernels

There are no other newforms in \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\).