Properties

Label 8.10.a.a
Level 8
Weight 10
Character orbit 8.a
Self dual Yes
Analytic conductor 4.120
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 8.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(4.12028668931\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q - 60q^{3} - 2074q^{5} - 4344q^{7} - 16083q^{9} + O(q^{10}) \) \( q - 60q^{3} - 2074q^{5} - 4344q^{7} - 16083q^{9} + 93644q^{11} - 12242q^{13} + 124440q^{15} - 319598q^{17} - 553516q^{19} + 260640q^{21} - 712936q^{23} + 2348351q^{25} + 2145960q^{27} + 2075838q^{29} - 6420448q^{31} - 5618640q^{33} + 9009456q^{35} - 18197754q^{37} + 734520q^{39} + 9033834q^{41} + 19594732q^{43} + 33356142q^{45} - 18484176q^{47} - 21483271q^{49} + 19175880q^{51} + 10255766q^{53} - 194217656q^{55} + 33210960q^{57} + 121666556q^{59} - 45948962q^{61} + 69864552q^{63} + 25389908q^{65} + 50535428q^{67} + 42776160q^{69} + 267044680q^{71} - 176213366q^{73} - 140901060q^{75} - 406789536q^{77} - 269685680q^{79} + 187804089q^{81} - 227032556q^{83} + 662846252q^{85} - 124550280q^{87} + 72141594q^{89} + 53179248q^{91} + 385226880q^{93} + 1147992184q^{95} + 228776546q^{97} - 1506076452q^{99} + O(q^{100}) \)

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 −60.0000 0 −2074.00 0 −4344.00 0 −16083.0 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 \( T_{3} + 60 \) acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(8))\).