Newform orbit 63.2.a.a

• Label: 63.2.a.a
• Level: $63$
• Weight: $2$
• Character orbit: 63.a
• Self dual: yes
• Analytic conductor: $0.503$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.503057532734\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 21)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

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

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

0

1.00000

0

−1.00000

2.00000

0

−1.00000

−3.00000

0

2.00000

Atkin-Lehner signs

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

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	63.2.a.a		1
3.b	odd	2	1		21.2.a.a	✓	1
4.b	odd	2	1		1008.2.a.l		1
5.b	even	2	1		1575.2.a.c		1
5.c	odd	4	2		1575.2.d.a		2
7.b	odd	2	1		441.2.a.f		1
7.c	even	3	2		441.2.e.a		2
7.d	odd	6	2		441.2.e.b		2
8.b	even	2	1		4032.2.a.h		1
8.d	odd	2	1		4032.2.a.k		1
9.c	even	3	2		567.2.f.b		2
9.d	odd	6	2		567.2.f.g		2
11.b	odd	2	1		7623.2.a.g		1
12.b	even	2	1		336.2.a.a		1
15.d	odd	2	1		525.2.a.d		1
15.e	even	4	2		525.2.d.a		2
21.c	even	2	1		147.2.a.a		1
21.g	even	6	2		147.2.e.c		2
21.h	odd	6	2		147.2.e.b		2
24.f	even	2	1		1344.2.a.s		1
24.h	odd	2	1		1344.2.a.g		1
28.d	even	2	1		7056.2.a.p		1
33.d	even	2	1		2541.2.a.j		1
39.d	odd	2	1		3549.2.a.c		1
48.i	odd	4	2		5376.2.c.r		2
48.k	even	4	2		5376.2.c.l		2
51.c	odd	2	1		6069.2.a.b		1
57.d	even	2	1		7581.2.a.d		1
60.h	even	2	1		8400.2.a.bn		1
84.h	odd	2	1		2352.2.a.v		1
84.j	odd	6	2		2352.2.q.e		2
84.n	even	6	2		2352.2.q.x		2
105.g	even	2	1		3675.2.a.n		1
168.e	odd	2	1		9408.2.a.m		1
168.i	even	2	1		9408.2.a.bv		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
21.2.a.a	✓	1	3.b	odd	2	1
63.2.a.a		1	1.a	even	1	1	trivial
147.2.a.a		1	21.c	even	2	1
147.2.e.b		2	21.h	odd	6	2
147.2.e.c		2	21.g	even	6	2
336.2.a.a		1	12.b	even	2	1
441.2.a.f		1	7.b	odd	2	1
441.2.e.a		2	7.c	even	3	2
441.2.e.b		2	7.d	odd	6	2
525.2.a.d		1	15.d	odd	2	1
525.2.d.a		2	15.e	even	4	2
567.2.f.b		2	9.c	even	3	2
567.2.f.g		2	9.d	odd	6	2
1008.2.a.l		1	4.b	odd	2	1
1344.2.a.g		1	24.h	odd	2	1
1344.2.a.s		1	24.f	even	2	1
1575.2.a.c		1	5.b	even	2	1
1575.2.d.a		2	5.c	odd	4	2
2352.2.a.v		1	84.h	odd	2	1
2352.2.q.e		2	84.j	odd	6	2
2352.2.q.x		2	84.n	even	6	2
2541.2.a.j		1	33.d	even	2	1
3549.2.a.c		1	39.d	odd	2	1
3675.2.a.n		1	105.g	even	2	1
4032.2.a.h		1	8.b	even	2	1
4032.2.a.k		1	8.d	odd	2	1
5376.2.c.l		2	48.k	even	4	2
5376.2.c.r		2	48.i	odd	4	2
6069.2.a.b		1	51.c	odd	2	1
7056.2.a.p		1	28.d	even	2	1
7581.2.a.d		1	57.d	even	2	1
7623.2.a.g		1	11.b	odd	2	1
8400.2.a.bn		1	60.h	even	2	1
9408.2.a.m		1	168.e	odd	2	1
9408.2.a.bv		1	168.i	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(63))\).

Hecke characteristic polynomials

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