Properties

Label 5520.2.a.bc
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

\(f(q)\) \(=\) \( q + q^{3} + q^{5} - 3q^{7} + q^{9} + O(q^{10}) \) \( q + q^{3} + q^{5} - 3q^{7} + q^{9} - 2q^{11} - 2q^{13} + q^{15} + 5q^{17} + 2q^{19} - 3q^{21} + q^{23} + q^{25} + q^{27} - 5q^{29} - 3q^{31} - 2q^{33} - 3q^{35} - 7q^{37} - 2q^{39} - 11q^{41} + 8q^{43} + q^{45} - 8q^{47} + 2q^{49} + 5q^{51} + 5q^{53} - 2q^{55} + 2q^{57} + q^{59} - 8q^{61} - 3q^{63} - 2q^{65} + 9q^{67} + q^{69} - q^{71} + 10q^{73} + q^{75} + 6q^{77} + q^{81} - 15q^{83} + 5q^{85} - 5q^{87} + 6q^{91} - 3q^{93} + 2q^{95} - 10q^{97} - 2q^{99} + O(q^{100}) \)

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 −3.00000 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.bc 1
4.b odd 2 1 345.2.a.f 1
12.b even 2 1 1035.2.a.a 1
20.d odd 2 1 1725.2.a.a 1
20.e even 4 2 1725.2.b.b 2
60.h even 2 1 5175.2.a.x 1
92.b even 2 1 7935.2.a.k 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
345.2.a.f 1 4.b odd 2 1
1035.2.a.a 1 12.b even 2 1
1725.2.a.a 1 20.d odd 2 1
1725.2.b.b 2 20.e even 4 2
5175.2.a.x 1 60.h even 2 1
5520.2.a.bc 1 1.a even 1 1 trivial
7935.2.a.k 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5520))\):

\( T_{7} + 3 \)
\( T_{11} + 2 \)
\( T_{13} + 2 \)
\( T_{17} - 5 \)
\( T_{19} - 2 \)

Hecke characteristic polynomials

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