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

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

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:

Atkin-Lehner signs

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

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

Hecke kernels

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 2 \) Copy content Toggle raw display
$3$ \( T + 3 \) Copy content Toggle raw display
$5$ \( T + 4 \) Copy content Toggle raw display
$7$ \( T + 4 \) Copy content Toggle raw display
$11$ \( T + 6 \) Copy content Toggle raw display
$13$ \( T + 4 \) Copy content Toggle raw display
$17$ \( T + 4 \) Copy content Toggle raw display
$19$ \( T + 7 \) Copy content Toggle raw display
$23$ \( T + 6 \) Copy content Toggle raw display
$29$ \( T + 6 \) Copy content Toggle raw display
$31$ \( T + 2 \) Copy content Toggle raw display
$37$ \( T \) Copy content Toggle raw display
$41$ \( T \) Copy content Toggle raw display
$43$ \( T + 8 \) Copy content Toggle raw display
$47$ \( T + 9 \) Copy content Toggle raw display
$53$ \( T + 9 \) Copy content Toggle raw display
$59$ \( T + 11 \) Copy content Toggle raw display
$61$ \( T + 2 \) Copy content Toggle raw display
$67$ \( T + 12 \) Copy content Toggle raw display
$71$ \( T + 8 \) Copy content Toggle raw display
$73$ \( T + 14 \) Copy content Toggle raw display
$79$ \( T - 9 \) Copy content Toggle raw display
$83$ \( T + 2 \) Copy content Toggle raw display
$89$ \( T - 11 \) Copy content Toggle raw display
$97$ \( T - 6 \) Copy content Toggle raw display
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