Properties

Label 8046.2.a.a
Level 8046
Weight 2
Character orbit 8046.a
Self dual Yes
Analytic conductor 64.248
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8046.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2476334663\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} + 2q^{5} + q^{7} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} + 2q^{5} + q^{7} - q^{8} - 2q^{10} - 2q^{13} - q^{14} + q^{16} + 4q^{17} + 4q^{19} + 2q^{20} - 5q^{23} - q^{25} + 2q^{26} + q^{28} + q^{29} - 5q^{31} - q^{32} - 4q^{34} + 2q^{35} - 6q^{37} - 4q^{38} - 2q^{40} - 9q^{41} - 4q^{43} + 5q^{46} - 6q^{47} - 6q^{49} + q^{50} - 2q^{52} + q^{53} - q^{56} - q^{58} + 2q^{59} - 6q^{61} + 5q^{62} + q^{64} - 4q^{65} + 4q^{68} - 2q^{70} - 3q^{71} - 6q^{73} + 6q^{74} + 4q^{76} - 8q^{79} + 2q^{80} + 9q^{82} + 6q^{83} + 8q^{85} + 4q^{86} + q^{89} - 2q^{91} - 5q^{92} + 6q^{94} + 8q^{95} + 10q^{97} + 6q^{98} + O(q^{100}) \)

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
−1.00000 0 1.00000 2.00000 0 1.00000 −1.00000 0 −2.00000
\(n\): 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
\(2\) \(1\)
\(3\) \(1\)
\(149\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8046))\):

\( T_{5} - 2 \)
\( T_{11} \)