Properties

Label 8015.2.a.a
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

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

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
−2.00000 −3.00000 2.00000 1.00000 6.00000 1.00000 0 6.00000 −2.00000
\(n\): 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8015))\):

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