Properties

Label 8041.2.a.b
Level 8041
Weight 2
Character orbit 8041.a
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
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

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

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
−1.00000 3.00000 −1.00000 −2.00000 −3.00000 −2.00000 3.00000 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
\(11\) \(1\)
\(17\) \(-1\)
\(43\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{2} + 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8041))\).