Properties

Label 5520.2.a.a
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 345)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{3} - q^{5} - 4q^{7} + q^{9} + O(q^{10}) \) \( q - q^{3} - q^{5} - 4q^{7} + q^{9} - 4q^{11} + 6q^{13} + q^{15} - 2q^{17} + 4q^{19} + 4q^{21} + q^{23} + q^{25} - q^{27} - 10q^{29} + 8q^{31} + 4q^{33} + 4q^{35} + 2q^{37} - 6q^{39} + 2q^{41} + 8q^{43} - q^{45} + 9q^{49} + 2q^{51} - 6q^{53} + 4q^{55} - 4q^{57} + 6q^{61} - 4q^{63} - 6q^{65} - 8q^{67} - q^{69} + 4q^{71} + 10q^{73} - q^{75} + 16q^{77} - 16q^{79} + q^{81} + 12q^{83} + 2q^{85} + 10q^{87} - 10q^{89} - 24q^{91} - 8q^{93} - 4q^{95} - 10q^{97} - 4q^{99} + O(q^{100}) \)

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
0 −1.00000 0 −1.00000 0 −4.00000 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.a 1
4.b odd 2 1 345.2.a.e 1
12.b even 2 1 1035.2.a.c 1
20.d odd 2 1 1725.2.a.b 1
20.e even 4 2 1725.2.b.f 2
60.h even 2 1 5175.2.a.q 1
92.b even 2 1 7935.2.a.j 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
345.2.a.e 1 4.b odd 2 1
1035.2.a.c 1 12.b even 2 1
1725.2.a.b 1 20.d odd 2 1
1725.2.b.f 2 20.e even 4 2
5175.2.a.q 1 60.h even 2 1
5520.2.a.a 1 1.a even 1 1 trivial
7935.2.a.j 1 92.b even 2 1

Hecke kernels

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

\( T_{7} + 4 \)
\( T_{11} + 4 \)
\( T_{13} - 6 \)
\( T_{17} + 2 \)
\( T_{19} - 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 1 + T \)
$5$ \( 1 + T \)
$7$ \( 4 + T \)
$11$ \( 4 + T \)
$13$ \( -6 + T \)
$17$ \( 2 + T \)
$19$ \( -4 + T \)
$23$ \( -1 + T \)
$29$ \( 10 + T \)
$31$ \( -8 + T \)
$37$ \( -2 + T \)
$41$ \( -2 + T \)
$43$ \( -8 + T \)
$47$ \( T \)
$53$ \( 6 + T \)
$59$ \( T \)
$61$ \( -6 + T \)
$67$ \( 8 + T \)
$71$ \( -4 + T \)
$73$ \( -10 + T \)
$79$ \( 16 + T \)
$83$ \( -12 + T \)
$89$ \( 10 + T \)
$97$ \( 10 + T \)
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