Newform orbit 5776.2.a.i

• Label: 5776.2.a.i
• Level: $5776$
• Weight: $2$
• Character orbit: 5776.a
• Self dual: yes
• Analytic conductor: $46.122$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -19
• Inner twists: $2$

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 361)
Fricke sign:	\(-1\)
Sato-Tate group:	$N(\mathrm{U}(1))$

$q$-expansion

\(f(q)\)

\(=\)

\( q - q^{5} - 3 q^{7} - 3 q^{9}+O(q^{10}) \)

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

0

0

−1.00000

0

−3.00000

0

−3.00000

0

Atkin-Lehner signs

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

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
19.b	odd	2	1	CM by \(\Q(\sqrt{-19}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	5776.2.a.i		1
4.b	odd	2	1		361.2.a.a	✓	1
12.b	even	2	1		3249.2.a.e		1
19.b	odd	2	1	CM	5776.2.a.i		1
20.d	odd	2	1		9025.2.a.f		1
76.d	even	2	1		361.2.a.a	✓	1
76.f	even	6	2		361.2.c.b		2
76.g	odd	6	2		361.2.c.b		2
76.k	even	18	6		361.2.e.c		6
76.l	odd	18	6		361.2.e.c		6
228.b	odd	2	1		3249.2.a.e		1
380.d	even	2	1		9025.2.a.f		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
361.2.a.a	✓	1	4.b	odd	2	1
361.2.a.a	✓	1	76.d	even	2	1
361.2.c.b		2	76.f	even	6	2
361.2.c.b		2	76.g	odd	6	2
361.2.e.c		6	76.k	even	18	6
361.2.e.c		6	76.l	odd	18	6
3249.2.a.e		1	12.b	even	2	1
3249.2.a.e		1	228.b	odd	2	1
5776.2.a.i		1	1.a	even	1	1	trivial
5776.2.a.i		1	19.b	odd	2	1	CM
9025.2.a.f		1	20.d	odd	2	1
9025.2.a.f		1	380.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5776))\):

\( T_{3} \)

\( T_{5} + 1 \)

\( T_{7} + 3 \)

\( T_{11} - 5 \)

\( T_{13} \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T \)
$3$	\( T \)
$5$	\( T + 1 \)
$7$	\( T + 3 \)
$11$	\( T - 5 \)