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

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

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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5520))\):

\( T_{7} + 4 \) Copy content Toggle raw display
\( T_{11} + 4 \) Copy content Toggle raw display
\( T_{13} - 6 \) Copy content Toggle raw display
\( T_{17} + 2 \) Copy content Toggle raw display
\( T_{19} - 4 \) Copy content Toggle raw display

Hecke characteristic polynomials

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