Properties

Label 5077.2.a.a
Level 5077
Weight 2
Character orbit 5077.a
Self dual yes
Analytic conductor 40.540
Analytic rank 3
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 5077 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5077.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(40.5400491062\)
Analytic rank: \(3\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{2} - 3q^{3} + 2q^{4} - 4q^{5} + 6q^{6} - 4q^{7} + 6q^{9} + O(q^{10}) \) \( q - 2q^{2} - 3q^{3} + 2q^{4} - 4q^{5} + 6q^{6} - 4q^{7} + 6q^{9} + 8q^{10} - 6q^{11} - 6q^{12} - 4q^{13} + 8q^{14} + 12q^{15} - 4q^{16} - 4q^{17} - 12q^{18} - 7q^{19} - 8q^{20} + 12q^{21} + 12q^{22} - 6q^{23} + 11q^{25} + 8q^{26} - 9q^{27} - 8q^{28} - 6q^{29} - 24q^{30} - 2q^{31} + 8q^{32} + 18q^{33} + 8q^{34} + 16q^{35} + 12q^{36} + 14q^{38} + 12q^{39} - 24q^{42} - 8q^{43} - 12q^{44} - 24q^{45} + 12q^{46} - 9q^{47} + 12q^{48} + 9q^{49} - 22q^{50} + 12q^{51} - 8q^{52} - 9q^{53} + 18q^{54} + 24q^{55} + 21q^{57} + 12q^{58} - 11q^{59} + 24q^{60} - 2q^{61} + 4q^{62} - 24q^{63} - 8q^{64} + 16q^{65} - 36q^{66} - 12q^{67} - 8q^{68} + 18q^{69} - 32q^{70} - 8q^{71} - 14q^{73} - 33q^{75} - 14q^{76} + 24q^{77} - 24q^{78} + 9q^{79} + 16q^{80} + 9q^{81} - 2q^{83} + 24q^{84} + 16q^{85} + 16q^{86} + 18q^{87} + 11q^{89} + 48q^{90} + 16q^{91} - 12q^{92} + 6q^{93} + 18q^{94} + 28q^{95} - 24q^{96} + 6q^{97} - 18q^{98} - 36q^{99} + O(q^{100}) \)

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 −4.00000 6.00000 −4.00000 0 6.00000 8.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5077.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5077.2.a.a 1 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(5077\) \(1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} + 2 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5077))\).