Properties

Label 5776.2.a.o
Level $5776$
Weight $2$
Character orbit 5776.a
Self dual yes
Analytic conductor $46.122$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5776 = 2^{4} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5776.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(46.1215922075\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 152)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} + 3q^{5} - 2q^{9} + O(q^{10}) \) \( q + q^{3} + 3q^{5} - 2q^{9} + 4q^{11} + 5q^{13} + 3q^{15} - 5q^{17} + q^{23} + 4q^{25} - 5q^{27} - 3q^{29} + 4q^{31} + 4q^{33} - 2q^{37} + 5q^{39} + 5q^{41} + 11q^{43} - 6q^{45} + 5q^{47} - 7q^{49} - 5q^{51} + 9q^{53} + 12q^{55} + 13q^{59} - q^{61} + 15q^{65} - 5q^{67} + q^{69} + q^{71} - 9q^{73} + 4q^{75} + 17q^{79} + q^{81} - 16q^{83} - 15q^{85} - 3q^{87} - 3q^{89} + 4q^{93} + 13q^{97} - 8q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(19\) \(-1\)

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 5776.2.a.o 1
4.b odd 2 1 2888.2.a.c 1
19.b odd 2 1 5776.2.a.h 1
19.d odd 6 2 304.2.i.b 2
57.f even 6 2 2736.2.s.q 2
76.d even 2 1 2888.2.a.e 1
76.f even 6 2 152.2.i.a 2
152.l odd 6 2 1216.2.i.e 2
152.o even 6 2 1216.2.i.i 2
228.n odd 6 2 1368.2.s.g 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
152.2.i.a 2 76.f even 6 2
304.2.i.b 2 19.d odd 6 2
1216.2.i.e 2 152.l odd 6 2
1216.2.i.i 2 152.o even 6 2
1368.2.s.g 2 228.n odd 6 2
2736.2.s.q 2 57.f even 6 2
2888.2.a.c 1 4.b odd 2 1
2888.2.a.e 1 76.d even 2 1
5776.2.a.h 1 19.b odd 2 1
5776.2.a.o 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5776))\):

\( T_{3} - 1 \)
\( T_{5} - 3 \)
\( T_{7} \)
\( T_{11} - 4 \)
\( T_{13} - 5 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -1 + T \)
$5$ \( -3 + T \)
$7$ \( T \)
$11$ \( -4 + T \)
$13$ \( -5 + T \)
$17$ \( 5 + T \)
$19$ \( T \)
$23$ \( -1 + T \)
$29$ \( 3 + T \)
$31$ \( -4 + T \)
$37$ \( 2 + T \)
$41$ \( -5 + T \)
$43$ \( -11 + T \)
$47$ \( -5 + T \)
$53$ \( -9 + T \)
$59$ \( -13 + T \)
$61$ \( 1 + T \)
$67$ \( 5 + T \)
$71$ \( -1 + T \)
$73$ \( 9 + T \)
$79$ \( -17 + T \)
$83$ \( 16 + T \)
$89$ \( 3 + T \)
$97$ \( -13 + T \)
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