Newform orbit 5808.2.a.bn

• Label: 5808.2.a.bn
• Level: $5808$
• Weight: $2$
• Character orbit: 5808.a
• Self dual: yes
• Analytic conductor: $46.377$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 5808 = 2^{4} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5808.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(46.3771134940\)
Analytic rank:	\(1\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{5}) \)
Defining polynomial:	\( x^{2} - x - 1 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 132)
Fricke sign:	\(+1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{5})\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q - q^{3} - \beta q^{5} + (2 \beta - 3) q^{7} + q^{9} +O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - q^{5} - 4 q^{7} + 2 q^{9}+O(q^{10}) \)

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

1.61803
−0.618034

0

−1.00000

0

−1.61803

0

0.236068

0

1.00000

0

1.2

0

−1.00000

0

0.618034

0

−4.23607

0

1.00000

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( -1 \)
\(3\)	\( +1 \)
\(11\)	\( -1 \)

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	5808.2.a.bn		2
4.b	odd	2	1		1452.2.a.m		2
11.b	odd	2	1		5808.2.a.bq		2
11.d	odd	10	2		528.2.y.i		4
12.b	even	2	1		4356.2.a.w		2
44.c	even	2	1		1452.2.a.l		2
44.g	even	10	2		132.2.i.a	✓	4
44.g	even	10	2		1452.2.i.c		4
44.h	odd	10	2		1452.2.i.f		4
44.h	odd	10	2		1452.2.i.g		4
132.d	odd	2	1		4356.2.a.r		2
132.n	odd	10	2		396.2.j.b		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
132.2.i.a	✓	4	44.g	even	10	2
396.2.j.b		4	132.n	odd	10	2
528.2.y.i		4	11.d	odd	10	2
1452.2.a.l		2	44.c	even	2	1
1452.2.a.m		2	4.b	odd	2	1
1452.2.i.c		4	44.g	even	10	2
1452.2.i.f		4	44.h	odd	10	2
1452.2.i.g		4	44.h	odd	10	2
4356.2.a.r		2	132.d	odd	2	1
4356.2.a.w		2	12.b	even	2	1
5808.2.a.bn		2	1.a	even	1	1	trivial
5808.2.a.bq		2	11.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5808))\):

\( T_{5}^{2} + T_{5} - 1 \)

\( T_{7}^{2} + 4T_{7} - 1 \)

\( T_{13}^{2} - 4T_{13} - 1 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( (T + 1)^{2} \)
$5$	\( T^{2} + T - 1 \)
$7$	\( T^{2} + 4T - 1 \)
$11$	\( T^{2} \)