Newform orbit 1183.2.c.c

• Label: 1183.2.c.c
• Level: $1183$
• Weight: $2$
• Character orbit: 1183.c
• Analytic conductor: $9.446$
• Analytic rank: $0$
• Dimension: $4$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.44630255912\)
Analytic rank:	\(0\)
Dimension:	\(4\)
Coefficient field:	\(\Q(i, \sqrt{5})\)
Defining polynomial:	\(x^{4} + 3 x^{2} + 1\)
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\beta_2,\beta_3\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q + ( \beta_{1} - \beta_{3} ) q^{2} + ( -1 + \beta_{2} ) q^{3} + 3 \beta_{2} q^{4} + ( \beta_{1} - \beta_{3} ) q^{5} + ( -3 \beta_{1} + 2 \beta_{3} ) q^{6} + \beta_{3} q^{7} + ( -4 \beta_{1} + \beta_{3} ) q^{8} + ( -1 - 3 \beta_{2} ) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4q - 6q^{3} - 6q^{4} + 2q^{9} + O(q^{10}) \)

Basis of coefficient ring in terms of a root \(\nu\) of \(x^{4} + 3 x^{2} + 1\):

\(\beta_{0}\)	\(=\)	\( 1 \)
\(\beta_{1}\)	\(=\)	\( \nu \)
\(\beta_{2}\)	\(=\)	\( \nu^{2} + 1 \)
\(\beta_{3}\)	\(=\)	\( \nu^{3} + 2 \nu \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\)	\(339\)	\(1016\)
\(\chi(n)\)	\(1\)	\(-1\)

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

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

337.1

	−	1.61803i
		0.618034i
	−	0.618034i
		1.61803i

−

2.61803i

−2.61803

−4.85410

−

2.61803i

6.85410i

1.00000i

7.47214i

3.85410

−6.85410

337.2

−

0.381966i

−0.381966

1.85410

−

0.381966i

0.145898i

1.00000i

−

1.47214i

−2.85410

−0.145898

337.3

0.381966i

−0.381966

1.85410

0.381966i

−

0.145898i

−

1.00000i

1.47214i

−2.85410

−0.145898

337.4

2.61803i

−2.61803

−4.85410

2.61803i

−

6.85410i

−

1.00000i

−

7.47214i

3.85410

−6.85410

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
13.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1183.2.c.c		4
13.b	even	2	1	inner	1183.2.c.c		4
13.d	odd	4	1		1183.2.a.c		2
13.d	odd	4	1		1183.2.a.g		2
13.f	odd	12	2		91.2.f.a	✓	4
39.k	even	12	2		819.2.o.c		4
52.l	even	12	2		1456.2.s.h		4
91.i	even	4	1		8281.2.a.n		2
91.i	even	4	1		8281.2.a.bb		2
91.w	even	12	2		637.2.g.c		4
91.x	odd	12	2		637.2.h.g		4
91.ba	even	12	2		637.2.h.f		4
91.bc	even	12	2		637.2.f.c		4
91.bd	odd	12	2		637.2.g.b		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
91.2.f.a	✓	4	13.f	odd	12	2
637.2.f.c		4	91.bc	even	12	2
637.2.g.b		4	91.bd	odd	12	2
637.2.g.c		4	91.w	even	12	2
637.2.h.f		4	91.ba	even	12	2
637.2.h.g		4	91.x	odd	12	2
819.2.o.c		4	39.k	even	12	2
1183.2.a.c		2	13.d	odd	4	1
1183.2.a.g		2	13.d	odd	4	1
1183.2.c.c		4	1.a	even	1	1	trivial
1183.2.c.c		4	13.b	even	2	1	inner
1456.2.s.h		4	52.l	even	12	2
8281.2.a.n		2	91.i	even	4	1
8281.2.a.bb		2	91.i	even	4	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{4} + 7 T_{2}^{2} + 1 \) acting on \(S_{2}^{\mathrm{new}}(1183, [\chi])\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( 1 + 7 T^{2} + T^{4} \)
$3$	\( ( 1 + 3 T + T^{2} )^{2} \)
$5$	\( 1 + 7 T^{2} + T^{4} \)
$7$	\( ( 1 + T^{2} )^{2} \)
$11$	\( 81 + 27 T^{2} + T^{4} \)