Newform orbit 66.2.a.b

• Label: 66.2.a.b
• Level: $66$
• Weight: $2$
• Character orbit: 66.a
• Self dual: yes
• Analytic conductor: $0.527$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	66.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.527012653340\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	yes
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

\( q + q^{2} - q^{3} + q^{4} + 2 q^{5} - q^{6} - 4 q^{7} + q^{8} + q^{9}+O(q^{10}) \)

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

0

1.00000

−1.00000

1.00000

2.00000

−1.00000

−4.00000

1.00000

1.00000

2.00000

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\(-1\)
\(3\)	\(1\)
\(11\)	\(1\)

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	66.2.a.b	✓	1
3.b	odd	2	1		198.2.a.a		1
4.b	odd	2	1		528.2.a.j		1
5.b	even	2	1		1650.2.a.k		1
5.c	odd	4	2		1650.2.c.e		2
7.b	odd	2	1		3234.2.a.t		1
8.b	even	2	1		2112.2.a.r		1
8.d	odd	2	1		2112.2.a.e		1
9.c	even	3	2		1782.2.e.e		2
9.d	odd	6	2		1782.2.e.v		2
11.b	odd	2	1		726.2.a.c		1
11.c	even	5	4		726.2.e.g		4
11.d	odd	10	4		726.2.e.o		4
12.b	even	2	1		1584.2.a.f		1
15.d	odd	2	1		4950.2.a.bu		1
15.e	even	4	2		4950.2.c.p		2
21.c	even	2	1		9702.2.a.x		1
24.f	even	2	1		6336.2.a.cj		1
24.h	odd	2	1		6336.2.a.bw		1
33.d	even	2	1		2178.2.a.g		1
44.c	even	2	1		5808.2.a.bc		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
66.2.a.b	✓	1	1.a	even	1	1	trivial
198.2.a.a		1	3.b	odd	2	1
528.2.a.j		1	4.b	odd	2	1
726.2.a.c		1	11.b	odd	2	1
726.2.e.g		4	11.c	even	5	4
726.2.e.o		4	11.d	odd	10	4
1584.2.a.f		1	12.b	even	2	1
1650.2.a.k		1	5.b	even	2	1
1650.2.c.e		2	5.c	odd	4	2
1782.2.e.e		2	9.c	even	3	2
1782.2.e.v		2	9.d	odd	6	2
2112.2.a.e		1	8.d	odd	2	1
2112.2.a.r		1	8.b	even	2	1
2178.2.a.g		1	33.d	even	2	1
3234.2.a.t		1	7.b	odd	2	1
4950.2.a.bu		1	15.d	odd	2	1
4950.2.c.p		2	15.e	even	4	2
5808.2.a.bc		1	44.c	even	2	1
6336.2.a.bw		1	24.h	odd	2	1
6336.2.a.cj		1	24.f	even	2	1
9702.2.a.x		1	21.c	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} - 2 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(66))\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T - 1 \)
$3$	\( T + 1 \)
$5$	\( T - 2 \)
$7$	\( T + 4 \)
$11$	\( T + 1 \)