Properties

Label 5880.2.a.t
Level $5880$
Weight $2$
Character orbit 5880.a
Self dual yes
Analytic conductor $46.952$
Analytic rank $0$
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: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 840)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} - q^{5} + q^{9} + O(q^{10}) \) \( q + q^{3} - q^{5} + q^{9} - 4q^{11} + 2q^{13} - q^{15} - 2q^{17} + 4q^{19} + q^{25} + q^{27} - 10q^{29} - 4q^{33} + 6q^{37} + 2q^{39} + 6q^{41} - 4q^{43} - q^{45} + 8q^{47} - 2q^{51} + 6q^{53} + 4q^{55} + 4q^{57} + 4q^{59} + 10q^{61} - 2q^{65} + 4q^{67} - 16q^{71} + 14q^{73} + q^{75} + 8q^{79} + q^{81} + 4q^{83} + 2q^{85} - 10q^{87} - 10q^{89} - 4q^{95} - 10q^{97} - 4q^{99} + O(q^{100}) \)

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 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.t 1
7.b odd 2 1 840.2.a.d 1
21.c even 2 1 2520.2.a.f 1
28.d even 2 1 1680.2.a.t 1
35.c odd 2 1 4200.2.a.bb 1
35.f even 4 2 4200.2.t.c 2
56.e even 2 1 6720.2.a.m 1
56.h odd 2 1 6720.2.a.bl 1
84.h odd 2 1 5040.2.a.l 1
140.c even 2 1 8400.2.a.l 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
840.2.a.d 1 7.b odd 2 1
1680.2.a.t 1 28.d even 2 1
2520.2.a.f 1 21.c even 2 1
4200.2.a.bb 1 35.c odd 2 1
4200.2.t.c 2 35.f even 4 2
5040.2.a.l 1 84.h odd 2 1
5880.2.a.t 1 1.a even 1 1 trivial
6720.2.a.m 1 56.e even 2 1
6720.2.a.bl 1 56.h odd 2 1
8400.2.a.l 1 140.c even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5880))\):

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -1 + T \)
$5$ \( 1 + T \)
$7$ \( T \)
$11$ \( 4 + T \)
$13$ \( -2 + T \)
$17$ \( 2 + T \)
$19$ \( -4 + T \)
$23$ \( T \)
$29$ \( 10 + T \)
$31$ \( T \)
$37$ \( -6 + T \)
$41$ \( -6 + T \)
$43$ \( 4 + T \)
$47$ \( -8 + T \)
$53$ \( -6 + T \)
$59$ \( -4 + T \)
$61$ \( -10 + T \)
$67$ \( -4 + T \)
$71$ \( 16 + T \)
$73$ \( -14 + T \)
$79$ \( -8 + T \)
$83$ \( -4 + T \)
$89$ \( 10 + T \)
$97$ \( 10 + T \)
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