Properties

Label 5610.2.a.k
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

\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - 3q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - 3q^{7} - q^{8} + q^{9} + q^{10} - q^{11} + q^{12} - 5q^{13} + 3q^{14} - q^{15} + q^{16} + q^{17} - q^{18} + 7q^{19} - q^{20} - 3q^{21} + q^{22} + 7q^{23} - q^{24} + q^{25} + 5q^{26} + q^{27} - 3q^{28} - 6q^{29} + q^{30} + 3q^{31} - q^{32} - q^{33} - q^{34} + 3q^{35} + q^{36} + 7q^{37} - 7q^{38} - 5q^{39} + q^{40} - 2q^{41} + 3q^{42} - 8q^{43} - q^{44} - q^{45} - 7q^{46} - 6q^{47} + q^{48} + 2q^{49} - q^{50} + q^{51} - 5q^{52} + 14q^{53} - q^{54} + q^{55} + 3q^{56} + 7q^{57} + 6q^{58} + 4q^{59} - q^{60} + 5q^{61} - 3q^{62} - 3q^{63} + q^{64} + 5q^{65} + q^{66} - 7q^{67} + q^{68} + 7q^{69} - 3q^{70} + 14q^{71} - q^{72} - 12q^{73} - 7q^{74} + q^{75} + 7q^{76} + 3q^{77} + 5q^{78} - 2q^{79} - q^{80} + q^{81} + 2q^{82} + 3q^{83} - 3q^{84} - q^{85} + 8q^{86} - 6q^{87} + q^{88} - 18q^{89} + q^{90} + 15q^{91} + 7q^{92} + 3q^{93} + 6q^{94} - 7q^{95} - q^{96} - 5q^{97} - 2q^{98} - q^{99} + O(q^{100}) \)

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 −3.00000 −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.k 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5610.2.a.k 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5610))\):

\( T_{7} + 3 \)
\( T_{13} + 5 \)
\( T_{19} - 7 \)
\( T_{23} - 7 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( -1 + T \)
$5$ \( 1 + T \)
$7$ \( 3 + T \)
$11$ \( 1 + T \)
$13$ \( 5 + T \)
$17$ \( -1 + T \)
$19$ \( -7 + T \)
$23$ \( -7 + T \)
$29$ \( 6 + T \)
$31$ \( -3 + T \)
$37$ \( -7 + T \)
$41$ \( 2 + T \)
$43$ \( 8 + T \)
$47$ \( 6 + T \)
$53$ \( -14 + T \)
$59$ \( -4 + T \)
$61$ \( -5 + T \)
$67$ \( 7 + T \)
$71$ \( -14 + T \)
$73$ \( 12 + T \)
$79$ \( 2 + T \)
$83$ \( -3 + T \)
$89$ \( 18 + T \)
$97$ \( 5 + T \)
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