Properties

Label 5610.2.a.e
Level $5610$
Weight $2$
Character orbit 5610.a
Self dual yes
Analytic conductor $44.796$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5610.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.7960755339\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 4q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 4q^{7} - q^{8} + q^{9} + q^{10} + q^{11} - q^{12} - 4q^{13} - 4q^{14} + q^{15} + q^{16} + q^{17} - q^{18} + 4q^{19} - q^{20} - 4q^{21} - q^{22} + q^{24} + q^{25} + 4q^{26} - q^{27} + 4q^{28} - 8q^{29} - q^{30} + 2q^{31} - q^{32} - q^{33} - q^{34} - 4q^{35} + q^{36} - 8q^{37} - 4q^{38} + 4q^{39} + q^{40} - 2q^{41} + 4q^{42} + q^{44} - q^{45} - 2q^{47} - q^{48} + 9q^{49} - q^{50} - q^{51} - 4q^{52} - 8q^{53} + q^{54} - q^{55} - 4q^{56} - 4q^{57} + 8q^{58} - 8q^{59} + q^{60} - 10q^{61} - 2q^{62} + 4q^{63} + q^{64} + 4q^{65} + q^{66} + 4q^{67} + q^{68} + 4q^{70} + 12q^{71} - q^{72} + 2q^{73} + 8q^{74} - q^{75} + 4q^{76} + 4q^{77} - 4q^{78} + 12q^{79} - q^{80} + q^{81} + 2q^{82} - 12q^{83} - 4q^{84} - q^{85} + 8q^{87} - q^{88} - 6q^{89} + q^{90} - 16q^{91} - 2q^{93} + 2q^{94} - 4q^{95} + q^{96} + 2q^{97} - 9q^{98} + q^{99} + O(q^{100}) \)

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
−1.00000 −1.00000 1.00000 −1.00000 1.00000 4.00000 −1.00000 1.00000 1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(1\)
\(5\) \(1\)
\(11\) \(-1\)
\(17\) \(-1\)

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 5610.2.a.e 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5610.2.a.e 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5610))\):

\( T_{7} - 4 \)
\( T_{13} + 4 \)
\( T_{19} - 4 \)
\( T_{23} \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( 1 + T \)
$5$ \( 1 + T \)
$7$ \( -4 + T \)
$11$ \( -1 + T \)
$13$ \( 4 + T \)
$17$ \( -1 + T \)
$19$ \( -4 + T \)
$23$ \( T \)
$29$ \( 8 + T \)
$31$ \( -2 + T \)
$37$ \( 8 + T \)
$41$ \( 2 + T \)
$43$ \( T \)
$47$ \( 2 + T \)
$53$ \( 8 + T \)
$59$ \( 8 + T \)
$61$ \( 10 + T \)
$67$ \( -4 + T \)
$71$ \( -12 + T \)
$73$ \( -2 + T \)
$79$ \( -12 + T \)
$83$ \( 12 + T \)
$89$ \( 6 + T \)
$97$ \( -2 + T \)
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