Properties

Label 8.8.a.b
Level 8
Weight 8
Character orbit 8.a
Self dual Yes
Analytic conductor 2.499
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(2.49908020387\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut +\mathstrut 44q^{3} \) \(\mathstrut +\mathstrut 430q^{5} \) \(\mathstrut -\mathstrut 1224q^{7} \) \(\mathstrut -\mathstrut 251q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 44q^{3} \) \(\mathstrut +\mathstrut 430q^{5} \) \(\mathstrut -\mathstrut 1224q^{7} \) \(\mathstrut -\mathstrut 251q^{9} \) \(\mathstrut -\mathstrut 3164q^{11} \) \(\mathstrut +\mathstrut 6118q^{13} \) \(\mathstrut +\mathstrut 18920q^{15} \) \(\mathstrut -\mathstrut 16270q^{17} \) \(\mathstrut -\mathstrut 5476q^{19} \) \(\mathstrut -\mathstrut 53856q^{21} \) \(\mathstrut +\mathstrut 1576q^{23} \) \(\mathstrut +\mathstrut 106775q^{25} \) \(\mathstrut -\mathstrut 107272q^{27} \) \(\mathstrut +\mathstrut 122838q^{29} \) \(\mathstrut +\mathstrut 251360q^{31} \) \(\mathstrut -\mathstrut 139216q^{33} \) \(\mathstrut -\mathstrut 526320q^{35} \) \(\mathstrut -\mathstrut 52338q^{37} \) \(\mathstrut +\mathstrut 269192q^{39} \) \(\mathstrut -\mathstrut 319398q^{41} \) \(\mathstrut +\mathstrut 710788q^{43} \) \(\mathstrut -\mathstrut 107930q^{45} \) \(\mathstrut +\mathstrut 284112q^{47} \) \(\mathstrut +\mathstrut 674633q^{49} \) \(\mathstrut -\mathstrut 715880q^{51} \) \(\mathstrut +\mathstrut 296062q^{53} \) \(\mathstrut -\mathstrut 1360520q^{55} \) \(\mathstrut -\mathstrut 240944q^{57} \) \(\mathstrut -\mathstrut 897548q^{59} \) \(\mathstrut -\mathstrut 884810q^{61} \) \(\mathstrut +\mathstrut 307224q^{63} \) \(\mathstrut +\mathstrut 2630740q^{65} \) \(\mathstrut +\mathstrut 4659692q^{67} \) \(\mathstrut +\mathstrut 69344q^{69} \) \(\mathstrut -\mathstrut 2710792q^{71} \) \(\mathstrut -\mathstrut 5670854q^{73} \) \(\mathstrut +\mathstrut 4698100q^{75} \) \(\mathstrut +\mathstrut 3872736q^{77} \) \(\mathstrut -\mathstrut 5124176q^{79} \) \(\mathstrut -\mathstrut 4171031q^{81} \) \(\mathstrut -\mathstrut 1563556q^{83} \) \(\mathstrut -\mathstrut 6996100q^{85} \) \(\mathstrut +\mathstrut 5404872q^{87} \) \(\mathstrut +\mathstrut 11605674q^{89} \) \(\mathstrut -\mathstrut 7488432q^{91} \) \(\mathstrut +\mathstrut 11059840q^{93} \) \(\mathstrut -\mathstrut 2354680q^{95} \) \(\mathstrut +\mathstrut 10931618q^{97} \) \(\mathstrut +\mathstrut 794164q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 44.0000 0 430.000 0 −1224.00 0 −251.000 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

This newform can be constructed as the kernel of the linear operator \(T_{3} \) \(\mathstrut -\mathstrut 44 \) acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(8))\).