Properties

Label 8008.2.a.e
Level 8008
Weight 2
Character orbit 8008.a
Self dual Yes
Analytic conductor 63.944
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
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

\(f(q)\) \(=\) \( q + 3q^{3} + q^{5} + q^{7} + 6q^{9} + O(q^{10}) \) \( q + 3q^{3} + q^{5} + q^{7} + 6q^{9} - q^{11} + q^{13} + 3q^{15} + 4q^{17} - 4q^{19} + 3q^{21} + q^{23} - 4q^{25} + 9q^{27} + 4q^{29} + 5q^{31} - 3q^{33} + q^{35} + 9q^{37} + 3q^{39} + 2q^{43} + 6q^{45} + q^{49} + 12q^{51} - 10q^{53} - q^{55} - 12q^{57} + 11q^{59} - 8q^{61} + 6q^{63} + q^{65} + q^{67} + 3q^{69} + q^{71} - 2q^{73} - 12q^{75} - q^{77} + 4q^{79} + 9q^{81} - 6q^{83} + 4q^{85} + 12q^{87} + 7q^{89} + q^{91} + 15q^{93} - 4q^{95} + q^{97} - 6q^{99} + O(q^{100}) \)

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 3.00000 0 1.00000 0 1.00000 0 6.00000 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
\(2\) \(-1\)
\(7\) \(-1\)
\(11\) \(1\)
\(13\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8008))\):

\( T_{3} - 3 \)
\( T_{5} - 1 \)
\( T_{17} - 4 \)