Properties

Label 8015.2.a.d
Level 8015
Weight 2
Character orbit 8015.a
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
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: \(0\)
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

\(f(q)\) \(=\) \( q + q^{2} - q^{4} + q^{5} + q^{7} - 3q^{8} - 3q^{9} + O(q^{10}) \) \( q + q^{2} - q^{4} + q^{5} + q^{7} - 3q^{8} - 3q^{9} + q^{10} - 4q^{11} + 2q^{13} + q^{14} - q^{16} - 6q^{17} - 3q^{18} - 4q^{19} - q^{20} - 4q^{22} + q^{25} + 2q^{26} - q^{28} - 10q^{29} + 8q^{31} + 5q^{32} - 6q^{34} + q^{35} + 3q^{36} - 2q^{37} - 4q^{38} - 3q^{40} - 6q^{41} + 8q^{43} + 4q^{44} - 3q^{45} + 8q^{47} + q^{49} + q^{50} - 2q^{52} + 6q^{53} - 4q^{55} - 3q^{56} - 10q^{58} + 12q^{59} - 2q^{61} + 8q^{62} - 3q^{63} + 7q^{64} + 2q^{65} - 4q^{67} + 6q^{68} + q^{70} + 9q^{72} + 14q^{73} - 2q^{74} + 4q^{76} - 4q^{77} - q^{80} + 9q^{81} - 6q^{82} + 16q^{83} - 6q^{85} + 8q^{86} + 12q^{88} - 6q^{89} - 3q^{90} + 2q^{91} + 8q^{94} - 4q^{95} + 2q^{97} + q^{98} + 12q^{99} + O(q^{100}) \)

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 0 −1.00000 1.00000 0 1.00000 −3.00000 −3.00000 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8015))\):

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