Properties

Label 6008.2.a.a
Level 6008
Weight 2
Character orbit 6008.a
Self dual Yes
Analytic conductor 47.974
Analytic rank 2
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(2\)
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

\(f(q)\) \(=\) \( q - 2q^{5} - 4q^{7} - 3q^{9} + O(q^{10}) \) \( q - 2q^{5} - 4q^{7} - 3q^{9} - q^{13} - 6q^{17} + 3q^{19} - 9q^{23} - q^{25} - 10q^{29} - 8q^{31} + 8q^{35} + 11q^{37} - 4q^{43} + 6q^{45} - 3q^{47} + 9q^{49} - q^{53} - 13q^{59} + 3q^{61} + 12q^{63} + 2q^{65} + 8q^{67} - 8q^{71} - 4q^{73} + 6q^{79} + 9q^{81} + 6q^{83} + 12q^{85} - 5q^{89} + 4q^{91} - 6q^{95} - 3q^{97} + O(q^{100}) \)

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 0 0 −2.00000 0 −4.00000 0 −3.00000 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
\(2\) \(1\)
\(751\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{3} \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6008))\).