Properties

Label 8015.2.a.e
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

\(f(q)\) \(=\) \( q + q^{2} + 2q^{3} - q^{4} - q^{5} + 2q^{6} - q^{7} - 3q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + 2q^{3} - q^{4} - q^{5} + 2q^{6} - q^{7} - 3q^{8} + q^{9} - q^{10} - q^{11} - 2q^{12} - 5q^{13} - q^{14} - 2q^{15} - q^{16} + 2q^{17} + q^{18} + 4q^{19} + q^{20} - 2q^{21} - q^{22} - 4q^{23} - 6q^{24} + q^{25} - 5q^{26} - 4q^{27} + q^{28} - 4q^{29} - 2q^{30} + 9q^{31} + 5q^{32} - 2q^{33} + 2q^{34} + q^{35} - q^{36} + 7q^{37} + 4q^{38} - 10q^{39} + 3q^{40} + q^{41} - 2q^{42} - 3q^{43} + q^{44} - q^{45} - 4q^{46} + 3q^{47} - 2q^{48} + q^{49} + q^{50} + 4q^{51} + 5q^{52} - 5q^{53} - 4q^{54} + q^{55} + 3q^{56} + 8q^{57} - 4q^{58} + 4q^{59} + 2q^{60} + 2q^{61} + 9q^{62} - q^{63} + 7q^{64} + 5q^{65} - 2q^{66} + 12q^{67} - 2q^{68} - 8q^{69} + q^{70} + 9q^{71} - 3q^{72} - 14q^{73} + 7q^{74} + 2q^{75} - 4q^{76} + q^{77} - 10q^{78} + 12q^{79} + q^{80} - 11q^{81} + q^{82} + 6q^{83} + 2q^{84} - 2q^{85} - 3q^{86} - 8q^{87} + 3q^{88} + 9q^{89} - q^{90} + 5q^{91} + 4q^{92} + 18q^{93} + 3q^{94} - 4q^{95} + 10q^{96} - 10q^{97} + q^{98} - q^{99} + O(q^{100}) \)

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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8015))\):

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