Properties

Label 8008.2.a.a
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

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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

\(f(q)\) \(=\) \( q - 2q^{3} - q^{5} + q^{7} + q^{9} + O(q^{10}) \) \( q - 2q^{3} - q^{5} + q^{7} + q^{9} - q^{11} - q^{13} + 2q^{15} - 6q^{17} - 7q^{19} - 2q^{21} + q^{23} - 4q^{25} + 4q^{27} - 5q^{29} - 7q^{31} + 2q^{33} - q^{35} - 2q^{37} + 2q^{39} + 6q^{41} + q^{43} - q^{45} + 7q^{47} + q^{49} + 12q^{51} - 13q^{53} + q^{55} + 14q^{57} + 6q^{61} + q^{63} + q^{65} - 14q^{67} - 2q^{69} - 6q^{71} - 3q^{73} + 8q^{75} - q^{77} - 11q^{79} - 11q^{81} - 13q^{83} + 6q^{85} + 10q^{87} + 9q^{89} - q^{91} + 14q^{93} + 7q^{95} + 17q^{97} - q^{99} + O(q^{100}) \)

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 −2.00000 0 −1.00000 0 1.00000 0 1.00000 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8008))\):

\( T_{3} + 2 \)
\( T_{5} + 1 \)
\( T_{17} + 6 \)