Properties

Label 1008.2.a.d
Level 1008
Weight 2
Character orbit 1008.a
Self dual Yes
Analytic conductor 8.049
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(8.04892052375\)
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

\(f(q)\) \(=\) \( q - 2q^{5} + q^{7} + O(q^{10}) \) \( q - 2q^{5} + q^{7} - 4q^{11} + 2q^{13} + 6q^{17} - 8q^{19} - q^{25} - 6q^{29} - 8q^{31} - 2q^{35} - 2q^{37} - 2q^{41} + 4q^{43} - 8q^{47} + q^{49} - 6q^{53} + 8q^{55} - 6q^{61} - 4q^{65} + 4q^{67} - 8q^{71} + 10q^{73} - 4q^{77} - 16q^{79} + 8q^{83} - 12q^{85} + 6q^{89} + 2q^{91} + 16q^{95} - 6q^{97} + O(q^{100}) \)

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 1.00000 0 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
\(2\) \(1\)
\(3\) \(-1\)
\(7\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1008))\):

\( T_{5} + 2 \)
\( T_{11} + 4 \)
\( T_{13} - 2 \)