Properties

Label 5776.2.a.m
Level $5776$
Weight $2$
Character orbit 5776.a
Self dual yes
Analytic conductor $46.122$
Analytic rank $1$
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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 38)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} + q^{7} - 2q^{9} + O(q^{10}) \) \( q + q^{3} + q^{7} - 2q^{9} + 6q^{11} - 5q^{13} + 3q^{17} + q^{21} - 3q^{23} - 5q^{25} - 5q^{27} - 9q^{29} - 4q^{31} + 6q^{33} - 2q^{37} - 5q^{39} - 8q^{43} - 6q^{49} + 3q^{51} + 3q^{53} + 9q^{59} - 10q^{61} - 2q^{63} + 5q^{67} - 3q^{69} - 6q^{71} - 7q^{73} - 5q^{75} + 6q^{77} - 10q^{79} + q^{81} + 6q^{83} - 9q^{87} + 12q^{89} - 5q^{91} - 4q^{93} + 10q^{97} - 12q^{99} + O(q^{100}) \)

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 0 0 1.00000 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.m 1
4.b odd 2 1 722.2.a.e 1
12.b even 2 1 6498.2.a.f 1
19.b odd 2 1 304.2.a.c 1
57.d even 2 1 2736.2.a.n 1
76.d even 2 1 38.2.a.a 1
76.f even 6 2 722.2.c.e 2
76.g odd 6 2 722.2.c.c 2
76.k even 18 6 722.2.e.f 6
76.l odd 18 6 722.2.e.e 6
95.d odd 2 1 7600.2.a.n 1
152.b even 2 1 1216.2.a.e 1
152.g odd 2 1 1216.2.a.m 1
228.b odd 2 1 342.2.a.e 1
380.d even 2 1 950.2.a.d 1
380.j odd 4 2 950.2.b.b 2
532.b odd 2 1 1862.2.a.b 1
836.h odd 2 1 4598.2.a.p 1
988.g even 2 1 6422.2.a.h 1
1140.p odd 2 1 8550.2.a.m 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
38.2.a.a 1 76.d even 2 1
304.2.a.c 1 19.b odd 2 1
342.2.a.e 1 228.b odd 2 1
722.2.a.e 1 4.b odd 2 1
722.2.c.c 2 76.g odd 6 2
722.2.c.e 2 76.f even 6 2
722.2.e.e 6 76.l odd 18 6
722.2.e.f 6 76.k even 18 6
950.2.a.d 1 380.d even 2 1
950.2.b.b 2 380.j odd 4 2
1216.2.a.e 1 152.b even 2 1
1216.2.a.m 1 152.g odd 2 1
1862.2.a.b 1 532.b odd 2 1
2736.2.a.n 1 57.d even 2 1
4598.2.a.p 1 836.h odd 2 1
5776.2.a.m 1 1.a even 1 1 trivial
6422.2.a.h 1 988.g even 2 1
6498.2.a.f 1 12.b even 2 1
7600.2.a.n 1 95.d odd 2 1
8550.2.a.m 1 1140.p odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5776))\):

\( T_{3} - 1 \)
\( T_{5} \)
\( T_{7} - 1 \)
\( T_{11} - 6 \)
\( T_{13} + 5 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -1 + T \)
$5$ \( T \)
$7$ \( -1 + T \)
$11$ \( -6 + T \)
$13$ \( 5 + T \)
$17$ \( -3 + T \)
$19$ \( T \)
$23$ \( 3 + T \)
$29$ \( 9 + T \)
$31$ \( 4 + T \)
$37$ \( 2 + T \)
$41$ \( T \)
$43$ \( 8 + T \)
$47$ \( T \)
$53$ \( -3 + T \)
$59$ \( -9 + T \)
$61$ \( 10 + T \)
$67$ \( -5 + T \)
$71$ \( 6 + T \)
$73$ \( 7 + T \)
$79$ \( 10 + T \)
$83$ \( -6 + T \)
$89$ \( -12 + T \)
$97$ \( -10 + T \)
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