Newform orbit 1183.2.a.d

• Label: 1183.2.a.d
• Level: $1183$
• Weight: $2$
• Character orbit: 1183.a
• Self dual: yes
• Analytic conductor: $9.446$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(9.44630255912\)
Analytic rank:	\(1\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{2}) \)
Defining polynomial:	\( x^{2} - 2 \)
Coefficient ring:	\(\Z[a_1, a_2]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	\(+1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

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

\(f(q)\)	\(=\)	\( q + \beta q^{2} + \beta q^{3} + (\beta - 3) q^{5} + 2 q^{6} - q^{7} - 2 \beta q^{8} - q^{9} +O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 6 q^{5} + 4 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) \)

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

−1.41421
1.41421

−1.41421

−1.41421

0

−4.41421

2.00000

−1.00000

2.82843

−1.00000

6.24264

1.2

1.41421

1.41421

0

−1.58579

2.00000

−1.00000

−2.82843

−1.00000

−2.24264

Atkin-Lehner signs

\( p \)	Sign
\(7\)	\( +1 \)
\(13\)	\( +1 \)

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	1183.2.a.d		2
7.b	odd	2	1		8281.2.a.v		2
13.b	even	2	1		91.2.a.c	✓	2
13.d	odd	4	2		1183.2.c.d		4
39.d	odd	2	1		819.2.a.h		2
52.b	odd	2	1		1456.2.a.q		2
65.d	even	2	1		2275.2.a.j		2
91.b	odd	2	1		637.2.a.g		2
91.r	even	6	2		637.2.e.f		4
91.s	odd	6	2		637.2.e.g		4
104.e	even	2	1		5824.2.a.bl		2
104.h	odd	2	1		5824.2.a.bk		2
273.g	even	2	1		5733.2.a.s		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
91.2.a.c	✓	2	13.b	even	2	1
637.2.a.g		2	91.b	odd	2	1
637.2.e.f		4	91.r	even	6	2
637.2.e.g		4	91.s	odd	6	2
819.2.a.h		2	39.d	odd	2	1
1183.2.a.d		2	1.a	even	1	1	trivial
1183.2.c.d		4	13.d	odd	4	2
1456.2.a.q		2	52.b	odd	2	1
2275.2.a.j		2	65.d	even	2	1
5733.2.a.s		2	273.g	even	2	1
5824.2.a.bk		2	104.h	odd	2	1
5824.2.a.bl		2	104.e	even	2	1
8281.2.a.v		2	7.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1183))\):

\( T_{2}^{2} - 2 \)

\( T_{11}^{2} - 18 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} - 2 \)
$3$	\( T^{2} - 2 \)
$5$	\( T^{2} + 6T + 7 \)
$7$	\( (T + 1)^{2} \)
$11$	\( T^{2} - 18 \)