Properties

Label 8015.2.a.f
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

Downloads

Learn more about

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

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

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

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