Properties

Label 4560.2.a.w
Level $4560$
Weight $2$
Character orbit 4560.a
Self dual yes
Analytic conductor $36.412$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4560.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.4117833217\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 285)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} + q^{5} - 4q^{7} + q^{9} + O(q^{10}) \) \( q + q^{3} + q^{5} - 4q^{7} + q^{9} - 4q^{11} + 2q^{13} + q^{15} + 2q^{17} + q^{19} - 4q^{21} + 4q^{23} + q^{25} + q^{27} - 2q^{29} - 4q^{33} - 4q^{35} - 6q^{37} + 2q^{39} - 6q^{41} - 8q^{43} + q^{45} + 12q^{47} + 9q^{49} + 2q^{51} - 14q^{53} - 4q^{55} + q^{57} - 4q^{59} + 14q^{61} - 4q^{63} + 2q^{65} + 4q^{67} + 4q^{69} - 14q^{73} + q^{75} + 16q^{77} - 16q^{79} + q^{81} + 2q^{85} - 2q^{87} - 6q^{89} - 8q^{91} + q^{95} - 10q^{97} - 4q^{99} + O(q^{100}) \)

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
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(-1\)
\(19\) \(-1\)

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 4560.2.a.w 1
4.b odd 2 1 285.2.a.c 1
12.b even 2 1 855.2.a.a 1
20.d odd 2 1 1425.2.a.c 1
20.e even 4 2 1425.2.c.f 2
60.h even 2 1 4275.2.a.j 1
76.d even 2 1 5415.2.a.e 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
285.2.a.c 1 4.b odd 2 1
855.2.a.a 1 12.b even 2 1
1425.2.a.c 1 20.d odd 2 1
1425.2.c.f 2 20.e even 4 2
4275.2.a.j 1 60.h even 2 1
4560.2.a.w 1 1.a even 1 1 trivial
5415.2.a.e 1 76.d even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4560))\):

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -1 + T \)
$5$ \( -1 + T \)
$7$ \( 4 + T \)
$11$ \( 4 + T \)
$13$ \( -2 + T \)
$17$ \( -2 + T \)
$19$ \( -1 + T \)
$23$ \( -4 + T \)
$29$ \( 2 + T \)
$31$ \( T \)
$37$ \( 6 + T \)
$41$ \( 6 + T \)
$43$ \( 8 + T \)
$47$ \( -12 + T \)
$53$ \( 14 + T \)
$59$ \( 4 + T \)
$61$ \( -14 + T \)
$67$ \( -4 + T \)
$71$ \( T \)
$73$ \( 14 + T \)
$79$ \( 16 + T \)
$83$ \( T \)
$89$ \( 6 + T \)
$97$ \( 10 + T \)
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