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

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

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 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 \(S_{6}^{\mathrm{new}}(\Gamma_0(8))\).