Newform orbit 5184.2.a.bo

• Label: 5184.2.a.bo
• Level: $5184$
• Weight: $2$
• Character orbit: 5184.a
• Self dual: yes
• Analytic conductor: $41.394$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 5184 = 2^{6} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5184.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(41.3944484078\)
Analytic rank:	\(1\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{33}) \)
Defining polynomial:	\( x^{2} - x - 8 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 72)
Fricke sign:	\(1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{33})\). We also show the integral \(q\)-expansion of the trace form.

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

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

3.37228
−2.37228

0

0

0

−3.37228

0

1.37228

0

0

0

1.2

0

0

0

2.37228

0

−4.37228

0

0

0

Atkin-Lehner signs

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

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	5184.2.a.bo		2
3.b	odd	2	1		5184.2.a.bs		2
4.b	odd	2	1		5184.2.a.bp		2
8.b	even	2	1		1296.2.a.p		2
8.d	odd	2	1		648.2.a.g		2
9.c	even	3	2		1728.2.i.j		4
9.d	odd	6	2		576.2.i.l		4
12.b	even	2	1		5184.2.a.bt		2
24.f	even	2	1		648.2.a.f		2
24.h	odd	2	1		1296.2.a.n		2
36.f	odd	6	2		1728.2.i.i		4
36.h	even	6	2		576.2.i.j		4
72.j	odd	6	2		144.2.i.d		4
72.l	even	6	2		72.2.i.b	✓	4
72.n	even	6	2		432.2.i.d		4
72.p	odd	6	2		216.2.i.b		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
72.2.i.b	✓	4	72.l	even	6	2
144.2.i.d		4	72.j	odd	6	2
216.2.i.b		4	72.p	odd	6	2
432.2.i.d		4	72.n	even	6	2
576.2.i.j		4	36.h	even	6	2
576.2.i.l		4	9.d	odd	6	2
648.2.a.f		2	24.f	even	2	1
648.2.a.g		2	8.d	odd	2	1
1296.2.a.n		2	24.h	odd	2	1
1296.2.a.p		2	8.b	even	2	1
1728.2.i.i		4	36.f	odd	6	2
1728.2.i.j		4	9.c	even	3	2
5184.2.a.bo		2	1.a	even	1	1	trivial
5184.2.a.bp		2	4.b	odd	2	1
5184.2.a.bs		2	3.b	odd	2	1
5184.2.a.bt		2	12.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5184))\):

\( T_{5}^{2} + T_{5} - 8 \)

\( T_{7}^{2} + 3T_{7} - 6 \)

\( T_{11} + 1 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} \)
$5$	\( T^{2} + T - 8 \)
$7$	\( T^{2} + 3T - 6 \)
$11$	\( (T + 1)^{2} \)