Newform orbit 1134.2.a.n

• Label: 1134.2.a.n
• Level: $1134$
• Weight: $2$
• Character orbit: 1134.a
• Self dual: yes
• Analytic conductor: $9.055$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(9.05503558921\)
Analytic rank:	\(0\)
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 126)
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.

\(f(q)\)	\(=\)	\( q + q^{2} + q^{4} + ( - \beta - 1) q^{5} + q^{7} + q^{8}+O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} - 3 q^{5} + 2 q^{7} + 2 q^{8}+O(q^{10}) \)

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

1.00000

0

1.00000

−4.37228

0

1.00000

1.00000

0

−4.37228

1.2

1.00000

0

1.00000

1.37228

0

1.00000

1.00000

0

1.37228

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\(-1\)
\(3\)	\(-1\)
\(7\)	\(-1\)

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	1134.2.a.n		2
3.b	odd	2	1		1134.2.a.k		2
4.b	odd	2	1		9072.2.a.bb		2
7.b	odd	2	1		7938.2.a.bs		2
9.c	even	3	2		378.2.f.c		4
9.d	odd	6	2		126.2.f.d	✓	4
12.b	even	2	1		9072.2.a.bm		2
21.c	even	2	1		7938.2.a.bh		2
36.f	odd	6	2		3024.2.r.f		4
36.h	even	6	2		1008.2.r.f		4
63.g	even	3	2		2646.2.h.k		4
63.h	even	3	2		2646.2.e.n		4
63.i	even	6	2		882.2.e.k		4
63.j	odd	6	2		882.2.e.l		4
63.k	odd	6	2		2646.2.h.l		4
63.l	odd	6	2		2646.2.f.j		4
63.n	odd	6	2		882.2.h.m		4
63.o	even	6	2		882.2.f.k		4
63.s	even	6	2		882.2.h.n		4
63.t	odd	6	2		2646.2.e.m		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
126.2.f.d	✓	4	9.d	odd	6	2
378.2.f.c		4	9.c	even	3	2
882.2.e.k		4	63.i	even	6	2
882.2.e.l		4	63.j	odd	6	2
882.2.f.k		4	63.o	even	6	2
882.2.h.m		4	63.n	odd	6	2
882.2.h.n		4	63.s	even	6	2
1008.2.r.f		4	36.h	even	6	2
1134.2.a.k		2	3.b	odd	2	1
1134.2.a.n		2	1.a	even	1	1	trivial
2646.2.e.m		4	63.t	odd	6	2
2646.2.e.n		4	63.h	even	3	2
2646.2.f.j		4	63.l	odd	6	2
2646.2.h.k		4	63.g	even	3	2
2646.2.h.l		4	63.k	odd	6	2
3024.2.r.f		4	36.f	odd	6	2
7938.2.a.bh		2	21.c	even	2	1
7938.2.a.bs		2	7.b	odd	2	1
9072.2.a.bb		2	4.b	odd	2	1
9072.2.a.bm		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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1134))\):

\( T_{5}^{2} + 3T_{5} - 6 \)

\( T_{11}^{2} + 3T_{11} - 6 \)

\( T_{13} - 2 \)

Hecke characteristic polynomials

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