Properties

Label 8007.2.a.a
Level 8007
Weight 2
Character orbit 8007.a
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
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

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

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 −1.00000 −1.00000 0 −1.00000 2.00000 −3.00000 1.00000 0
\(n\): 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
\(3\) \(1\)
\(17\) \(-1\)
\(157\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{2} - 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8007))\).