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

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

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 −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 \(T_{3} \) \(\mathstrut +\mathstrut 60 \) acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(8))\).