Properties

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

Related objects

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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: \(1\)
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

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

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 −2.00000 2.00000 2.00000 4.00000 3.00000 0 1.00000 −4.00000
\(n\): 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 \( T_{2} + 2 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8041))\).