Properties

Label 8027.2.a.a
Level 8027
Weight 2
Character orbit 8027.a
Self dual Yes
Analytic conductor 64.096
Analytic rank 2
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(2\)
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

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

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 0 6.00000 −1.00000 0 6.00000 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
\(23\) \(-1\)
\(349\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{2} + 2 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8027))\).