Properties

Label 8015.2.a.c
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

Related objects

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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

\(f(q)\) \(=\) \( q - q^{2} + q^{3} - q^{4} + q^{5} - q^{6} + q^{7} + 3q^{8} - 2q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} - q^{4} + q^{5} - q^{6} + q^{7} + 3q^{8} - 2q^{9} - q^{10} - q^{12} + 5q^{13} - q^{14} + q^{15} - q^{16} + 2q^{18} - 8q^{19} - q^{20} + q^{21} + 6q^{23} + 3q^{24} + q^{25} - 5q^{26} - 5q^{27} - q^{28} - q^{30} - 5q^{32} + q^{35} + 2q^{36} + 2q^{37} + 8q^{38} + 5q^{39} + 3q^{40} - 8q^{41} - q^{42} - 8q^{43} - 2q^{45} - 6q^{46} - 10q^{47} - q^{48} + q^{49} - q^{50} - 5q^{52} - 2q^{53} + 5q^{54} + 3q^{56} - 8q^{57} + 3q^{59} - q^{60} + 5q^{61} - 2q^{63} + 7q^{64} + 5q^{65} - 6q^{67} + 6q^{69} - q^{70} - 6q^{71} - 6q^{72} - 11q^{73} - 2q^{74} + q^{75} + 8q^{76} - 5q^{78} + 3q^{79} - q^{80} + q^{81} + 8q^{82} + 7q^{83} - q^{84} + 8q^{86} + 10q^{89} + 2q^{90} + 5q^{91} - 6q^{92} + 10q^{94} - 8q^{95} - 5q^{96} - 8q^{97} - q^{98} + O(q^{100}) \)

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 1.00000 −1.00000 1.00000 −1.00000 1.00000 3.00000 −2.00000 −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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8015))\):

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