Properties

Label 5520.2.a.g
Level $5520$
Weight $2$
Character orbit 5520.a
Self dual yes
Analytic conductor $44.077$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5520.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.0774219157\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1380)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{3} - q^{5} + q^{7} + q^{9} + O(q^{10}) \) \( q - q^{3} - q^{5} + q^{7} + q^{9} - 4q^{13} + q^{15} - 3q^{17} + 4q^{19} - q^{21} + q^{23} + q^{25} - q^{27} - 3q^{29} + 7q^{31} - q^{35} + 11q^{37} + 4q^{39} - 9q^{41} + 4q^{43} - q^{45} - 6q^{47} - 6q^{49} + 3q^{51} + 9q^{53} - 4q^{57} - 3q^{59} - 10q^{61} + q^{63} + 4q^{65} + 13q^{67} - q^{69} - 9q^{71} - 16q^{73} - q^{75} - 8q^{79} + q^{81} + 15q^{83} + 3q^{85} + 3q^{87} - 4q^{91} - 7q^{93} - 4q^{95} + 2q^{97} + O(q^{100}) \)

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
0 −1.00000 0 −1.00000 0 1.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)
\(5\) \(1\)
\(23\) \(-1\)

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 5520.2.a.g 1
4.b odd 2 1 1380.2.a.c 1
12.b even 2 1 4140.2.a.i 1
20.d odd 2 1 6900.2.a.b 1
20.e even 4 2 6900.2.f.e 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1380.2.a.c 1 4.b odd 2 1
4140.2.a.i 1 12.b even 2 1
5520.2.a.g 1 1.a even 1 1 trivial
6900.2.a.b 1 20.d odd 2 1
6900.2.f.e 2 20.e even 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5520))\):

\( T_{7} - 1 \)
\( T_{11} \)
\( T_{13} + 4 \)
\( T_{17} + 3 \)
\( T_{19} - 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 1 + T \)
$5$ \( 1 + T \)
$7$ \( -1 + T \)
$11$ \( T \)
$13$ \( 4 + T \)
$17$ \( 3 + T \)
$19$ \( -4 + T \)
$23$ \( -1 + T \)
$29$ \( 3 + T \)
$31$ \( -7 + T \)
$37$ \( -11 + T \)
$41$ \( 9 + T \)
$43$ \( -4 + T \)
$47$ \( 6 + T \)
$53$ \( -9 + T \)
$59$ \( 3 + T \)
$61$ \( 10 + T \)
$67$ \( -13 + T \)
$71$ \( 9 + T \)
$73$ \( 16 + T \)
$79$ \( 8 + T \)
$83$ \( -15 + T \)
$89$ \( T \)
$97$ \( -2 + T \)
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