Properties

Label 8.6.a.a
Level 8
Weight 6
Character orbit 8.a
Self dual Yes
Analytic conductor 1.283
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 8.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.2830705585\)
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

\(f(q)\) \(=\) \( q + 20q^{3} - 74q^{5} - 24q^{7} + 157q^{9} + O(q^{10}) \) \( q + 20q^{3} - 74q^{5} - 24q^{7} + 157q^{9} + 124q^{11} + 478q^{13} - 1480q^{15} - 1198q^{17} + 3044q^{19} - 480q^{21} + 184q^{23} + 2351q^{25} - 1720q^{27} - 3282q^{29} - 5728q^{31} + 2480q^{33} + 1776q^{35} + 10326q^{37} + 9560q^{39} - 8886q^{41} - 9188q^{43} - 11618q^{45} + 23664q^{47} - 16231q^{49} - 23960q^{51} + 11686q^{53} - 9176q^{55} + 60880q^{57} + 16876q^{59} - 18482q^{61} - 3768q^{63} - 35372q^{65} - 15532q^{67} + 3680q^{69} - 31960q^{71} - 4886q^{73} + 47020q^{75} - 2976q^{77} + 44560q^{79} - 72551q^{81} + 67364q^{83} + 88652q^{85} - 65640q^{87} + 71994q^{89} - 11472q^{91} - 114560q^{93} - 225256q^{95} + 48866q^{97} + 19468q^{99} + O(q^{100}) \)

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 20.0000 0 −74.0000 0 −24.0000 0 157.000 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 \(S_{6}^{\mathrm{new}}(\Gamma_0(8))\).