Properties

Label 572.2.a.a
Level $572$
Weight $2$
Character orbit 572.a
Self dual yes
Analytic conductor $4.567$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(4.56744299562\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} + 3q^{5} + 2q^{7} - 2q^{9} + O(q^{10}) \) \( q + q^{3} + 3q^{5} + 2q^{7} - 2q^{9} + q^{11} + q^{13} + 3q^{15} + 2q^{19} + 2q^{21} - 3q^{23} + 4q^{25} - 5q^{27} - 6q^{29} - q^{31} + q^{33} + 6q^{35} - 7q^{37} + q^{39} + 6q^{41} + 8q^{43} - 6q^{45} + 12q^{47} - 3q^{49} - 6q^{53} + 3q^{55} + 2q^{57} + 9q^{59} + 2q^{61} - 4q^{63} + 3q^{65} - 7q^{67} - 3q^{69} - 3q^{71} + 8q^{73} + 4q^{75} + 2q^{77} - 4q^{79} + q^{81} - 12q^{83} - 6q^{87} - 15q^{89} + 2q^{91} - q^{93} + 6q^{95} - 13q^{97} - 2q^{99} + O(q^{100}) \)

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 3.00000 0 2.00000 0 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(11\) \(-1\)
\(13\) \(-1\)

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 572.2.a.a 1
3.b odd 2 1 5148.2.a.a 1
4.b odd 2 1 2288.2.a.g 1
8.b even 2 1 9152.2.a.i 1
8.d odd 2 1 9152.2.a.r 1
11.b odd 2 1 6292.2.a.j 1
13.b even 2 1 7436.2.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
572.2.a.a 1 1.a even 1 1 trivial
2288.2.a.g 1 4.b odd 2 1
5148.2.a.a 1 3.b odd 2 1
6292.2.a.j 1 11.b odd 2 1
7436.2.a.c 1 13.b even 2 1
9152.2.a.i 1 8.b even 2 1
9152.2.a.r 1 8.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(572))\):

\( T_{3} - 1 \)
\( T_{5} - 3 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -1 + T \)
$5$ \( -3 + T \)
$7$ \( -2 + T \)
$11$ \( -1 + T \)
$13$ \( -1 + T \)
$17$ \( T \)
$19$ \( -2 + T \)
$23$ \( 3 + T \)
$29$ \( 6 + T \)
$31$ \( 1 + T \)
$37$ \( 7 + T \)
$41$ \( -6 + T \)
$43$ \( -8 + T \)
$47$ \( -12 + T \)
$53$ \( 6 + T \)
$59$ \( -9 + T \)
$61$ \( -2 + T \)
$67$ \( 7 + T \)
$71$ \( 3 + T \)
$73$ \( -8 + T \)
$79$ \( 4 + T \)
$83$ \( 12 + T \)
$89$ \( 15 + T \)
$97$ \( 13 + T \)
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