Properties

Label 8015.2.a.b
Level 8015
Weight 2
Character orbit 8015.a
Self dual Yes
Analytic conductor 64.000
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
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

\(f(q)\) \(=\) \( q - q^{2} - 2q^{3} - q^{4} + q^{5} + 2q^{6} + q^{7} + 3q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - 2q^{3} - q^{4} + q^{5} + 2q^{6} + q^{7} + 3q^{8} + q^{9} - q^{10} + 3q^{11} + 2q^{12} - 7q^{13} - q^{14} - 2q^{15} - q^{16} + 6q^{17} - q^{18} + 4q^{19} - q^{20} - 2q^{21} - 3q^{22} - 6q^{24} + q^{25} + 7q^{26} + 4q^{27} - q^{28} + 2q^{30} - 9q^{31} - 5q^{32} - 6q^{33} - 6q^{34} + q^{35} - q^{36} - q^{37} - 4q^{38} + 14q^{39} + 3q^{40} - 5q^{41} + 2q^{42} + q^{43} - 3q^{44} + q^{45} + 5q^{47} + 2q^{48} + q^{49} - q^{50} - 12q^{51} + 7q^{52} - 5q^{53} - 4q^{54} + 3q^{55} + 3q^{56} - 8q^{57} - 12q^{59} + 2q^{60} + 14q^{61} + 9q^{62} + q^{63} + 7q^{64} - 7q^{65} + 6q^{66} - 6q^{68} - q^{70} - 3q^{71} + 3q^{72} - 2q^{73} + q^{74} - 2q^{75} - 4q^{76} + 3q^{77} - 14q^{78} - 12q^{79} - q^{80} - 11q^{81} + 5q^{82} - 2q^{83} + 2q^{84} + 6q^{85} - q^{86} + 9q^{88} - 5q^{89} - q^{90} - 7q^{91} + 18q^{93} - 5q^{94} + 4q^{95} + 10q^{96} - 2q^{97} - q^{98} + 3q^{99} + O(q^{100}) \)

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
−1.00000 −2.00000 −1.00000 1.00000 2.00000 1.00000 3.00000 1.00000 −1.00000
\(n\): 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
\(5\) \(-1\)
\(7\) \(-1\)
\(229\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8015))\):

\( T_{2} + 1 \)
\( T_{3} + 2 \)