Properties

Label 8004.2.a.a
Level 8004
Weight 2
Character orbit 8004.a
Self dual yes
Analytic conductor 63.912
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8004.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{3} - 2q^{5} - 5q^{7} + q^{9} + O(q^{10}) \) \( q - q^{3} - 2q^{5} - 5q^{7} + q^{9} - 3q^{11} + q^{13} + 2q^{15} - 3q^{17} + 6q^{19} + 5q^{21} - q^{23} - q^{25} - q^{27} + q^{29} + 2q^{31} + 3q^{33} + 10q^{35} + 6q^{37} - q^{39} - 2q^{41} + 6q^{43} - 2q^{45} + 7q^{47} + 18q^{49} + 3q^{51} - 4q^{53} + 6q^{55} - 6q^{57} - 2q^{61} - 5q^{63} - 2q^{65} + 9q^{67} + q^{69} - 10q^{73} + q^{75} + 15q^{77} + q^{81} + 2q^{83} + 6q^{85} - q^{87} - 9q^{89} - 5q^{91} - 2q^{93} - 12q^{95} + 6q^{97} - 3q^{99} + O(q^{100}) \)

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 −1.00000 0 −2.00000 0 −5.00000 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.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 8004.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8004.2.a.a 1 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)
\(23\) \(1\)
\(29\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8004))\):

\( T_{5} + 2 \)
\( T_{7} + 5 \)