Properties

Label 8027.2.a.b
Level 8027
Weight 2
Character orbit 8027.a
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
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

\(f(q)\) \(=\) \( q + q^{3} - 2q^{4} - q^{7} - 2q^{9} + O(q^{10}) \) \( q + q^{3} - 2q^{4} - q^{7} - 2q^{9} + 3q^{11} - 2q^{12} - 4q^{13} + 4q^{16} + 2q^{19} - q^{21} - q^{23} - 5q^{25} - 5q^{27} + 2q^{28} - 3q^{29} + 5q^{31} + 3q^{33} + 4q^{36} + 2q^{37} - 4q^{39} - 3q^{41} - q^{43} - 6q^{44} - 6q^{47} + 4q^{48} - 6q^{49} + 8q^{52} + 9q^{53} + 2q^{57} - q^{61} + 2q^{63} - 8q^{64} + 14q^{67} - q^{69} + 6q^{71} + 2q^{73} - 5q^{75} - 4q^{76} - 3q^{77} - q^{79} + q^{81} + 2q^{84} - 3q^{87} - 6q^{89} + 4q^{91} + 2q^{92} + 5q^{93} - 10q^{97} - 6q^{99} + O(q^{100}) \)

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 −2.00000 0 0 −1.00000 0 −2.00000 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
\(23\) \(1\)
\(349\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{2} \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8027))\).