Newform orbit 1156.2.a.c

• Label: 1156.2.a.c
• Level: $1156$
• Weight: $2$
• Character orbit: 1156.a
• Self dual: yes
• Analytic conductor: $9.231$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1156 = 2^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1156.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(9.23070647366\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{2}) \)
Defining polynomial:	\( x^{2} - 2 \)
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 68)
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.

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

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

0

−1.41421

0

−2.82843

0

−4.24264

0

−1.00000

0

1.2

0

1.41421

0

2.82843

0

4.24264

0

−1.00000

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\(-1\)
\(17\)	\(1\)

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1156.2.a.c		2
4.b	odd	2	1		4624.2.a.n		2
17.b	even	2	1	inner	1156.2.a.c		2
17.c	even	4	2		68.2.b.a	✓	2
17.d	even	8	2		1156.2.e.a		2
17.d	even	8	2		1156.2.e.b		2
17.e	odd	16	8		1156.2.h.d		8
51.f	odd	4	2		612.2.b.a		2
68.d	odd	2	1		4624.2.a.n		2
68.f	odd	4	2		272.2.b.c		2
85.f	odd	4	2		1700.2.g.a		4
85.i	odd	4	2		1700.2.g.a		4
85.j	even	4	2		1700.2.c.a		2
119.f	odd	4	2		3332.2.b.a		2
136.i	even	4	2		1088.2.b.e		2
136.j	odd	4	2		1088.2.b.f		2
204.l	even	4	2		2448.2.c.d		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
68.2.b.a	✓	2	17.c	even	4	2
272.2.b.c		2	68.f	odd	4	2
612.2.b.a		2	51.f	odd	4	2
1088.2.b.e		2	136.i	even	4	2
1088.2.b.f		2	136.j	odd	4	2
1156.2.a.c		2	1.a	even	1	1	trivial
1156.2.a.c		2	17.b	even	2	1	inner
1156.2.e.a		2	17.d	even	8	2
1156.2.e.b		2	17.d	even	8	2
1156.2.h.d		8	17.e	odd	16	8
1700.2.c.a		2	85.j	even	4	2
1700.2.g.a		4	85.f	odd	4	2
1700.2.g.a		4	85.i	odd	4	2
2448.2.c.d		2	204.l	even	4	2
3332.2.b.a		2	119.f	odd	4	2
4624.2.a.n		2	4.b	odd	2	1
4624.2.a.n		2	68.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{2} - 2 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1156))\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} - 2 \)
$5$	\( T^{2} - 8 \)
$7$	\( T^{2} - 18 \)
$11$	\( T^{2} - 2 \)