Properties

Label 5880.2.a.a
Level $5880$
Weight $2$
Character orbit 5880.a
Self dual yes
Analytic conductor $46.952$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5880 = 2^{3} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5880.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(46.9520363885\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 120)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{3} - q^{5} + q^{9} + O(q^{10}) \) \( q - q^{3} - q^{5} + q^{9} - 4q^{11} - 6q^{13} + q^{15} + 6q^{17} + 4q^{19} + q^{25} - q^{27} - 2q^{29} + 8q^{31} + 4q^{33} - 2q^{37} + 6q^{39} + 6q^{41} + 12q^{43} - q^{45} - 8q^{47} - 6q^{51} + 6q^{53} + 4q^{55} - 4q^{57} - 12q^{59} - 14q^{61} + 6q^{65} + 4q^{67} + 8q^{71} + 6q^{73} - q^{75} - 8q^{79} + q^{81} + 12q^{83} - 6q^{85} + 2q^{87} - 10q^{89} - 8q^{93} - 4q^{95} - 2q^{97} - 4q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)
\(5\) \(1\)
\(7\) \(-1\)

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 5880.2.a.a 1
7.b odd 2 1 120.2.a.b 1
21.c even 2 1 360.2.a.b 1
28.d even 2 1 240.2.a.c 1
35.c odd 2 1 600.2.a.c 1
35.f even 4 2 600.2.f.b 2
56.e even 2 1 960.2.a.j 1
56.h odd 2 1 960.2.a.c 1
63.l odd 6 2 3240.2.q.g 2
63.o even 6 2 3240.2.q.q 2
84.h odd 2 1 720.2.a.d 1
105.g even 2 1 1800.2.a.n 1
105.k odd 4 2 1800.2.f.j 2
112.j even 4 2 3840.2.k.j 2
112.l odd 4 2 3840.2.k.o 2
140.c even 2 1 1200.2.a.o 1
140.j odd 4 2 1200.2.f.g 2
168.e odd 2 1 2880.2.a.bb 1
168.i even 2 1 2880.2.a.x 1
280.c odd 2 1 4800.2.a.cd 1
280.n even 2 1 4800.2.a.r 1
280.s even 4 2 4800.2.f.bc 2
280.y odd 4 2 4800.2.f.i 2
420.o odd 2 1 3600.2.a.t 1
420.w even 4 2 3600.2.f.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
120.2.a.b 1 7.b odd 2 1
240.2.a.c 1 28.d even 2 1
360.2.a.b 1 21.c even 2 1
600.2.a.c 1 35.c odd 2 1
600.2.f.b 2 35.f even 4 2
720.2.a.d 1 84.h odd 2 1
960.2.a.c 1 56.h odd 2 1
960.2.a.j 1 56.e even 2 1
1200.2.a.o 1 140.c even 2 1
1200.2.f.g 2 140.j odd 4 2
1800.2.a.n 1 105.g even 2 1
1800.2.f.j 2 105.k odd 4 2
2880.2.a.x 1 168.i even 2 1
2880.2.a.bb 1 168.e odd 2 1
3240.2.q.g 2 63.l odd 6 2
3240.2.q.q 2 63.o even 6 2
3600.2.a.t 1 420.o odd 2 1
3600.2.f.c 2 420.w even 4 2
3840.2.k.j 2 112.j even 4 2
3840.2.k.o 2 112.l odd 4 2
4800.2.a.r 1 280.n even 2 1
4800.2.a.cd 1 280.c odd 2 1
4800.2.f.i 2 280.y odd 4 2
4800.2.f.bc 2 280.s even 4 2
5880.2.a.a 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5880))\):

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 1 + T \)
$5$ \( 1 + T \)
$7$ \( T \)
$11$ \( 4 + T \)
$13$ \( 6 + T \)
$17$ \( -6 + T \)
$19$ \( -4 + T \)
$23$ \( T \)
$29$ \( 2 + T \)
$31$ \( -8 + T \)
$37$ \( 2 + T \)
$41$ \( -6 + T \)
$43$ \( -12 + T \)
$47$ \( 8 + T \)
$53$ \( -6 + T \)
$59$ \( 12 + T \)
$61$ \( 14 + T \)
$67$ \( -4 + T \)
$71$ \( -8 + T \)
$73$ \( -6 + T \)
$79$ \( 8 + T \)
$83$ \( -12 + T \)
$89$ \( 10 + T \)
$97$ \( 2 + T \)
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