Newform orbit 63.3.d.a

• Label: 63.3.d.a
• Level: $63$
• Weight: $3$
• Character orbit: 63.d
• Self dual: yes
• Analytic conductor: $1.717$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -7
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(1.71662566547\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\)

\(=\)

q + 3 * q^2 + 5 * q^4 - 7 * q^7 + 3 * q^8 + 6 * q^11 - 21 * q^14 - 11 * q^16 + 18 * q^22 - 18 * q^23 + 25 * q^25 - 35 * q^28 + 54 * q^29 - 45 * q^32 - 38 * q^37 + 58 * q^43 + 30 * q^44 - 54 * q^46 + 49 * q^49 + 75 * q^50 + 6 * q^53 - 21 * q^56 + 162 * q^58 - 91 * q^64 - 118 * q^67 - 114 * q^71 - 114 * q^74 - 42 * q^77 - 94 * q^79 + 174 * q^86 + 18 * q^88 - 90 * q^92 + 147 * q^98

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\)	\(10\)	\(29\)
\(\chi(n)\)	\(-1\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

55.1

0

3.00000

0

5.00000

0

0

−7.00000

3.00000

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	CM by \(\Q(\sqrt{-7}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	63.3.d.a		1
3.b	odd	2	1		7.3.b.a	✓	1
4.b	odd	2	1		1008.3.f.a		1
7.b	odd	2	1	CM	63.3.d.a		1
7.c	even	3	2		441.3.m.a		2
7.d	odd	6	2		441.3.m.a		2
12.b	even	2	1		112.3.c.a		1
15.d	odd	2	1		175.3.d.a		1
15.e	even	4	2		175.3.c.a		2
21.c	even	2	1		7.3.b.a	✓	1
21.g	even	6	2		49.3.d.a		2
21.h	odd	6	2		49.3.d.a		2
24.f	even	2	1		448.3.c.b		1
24.h	odd	2	1		448.3.c.a		1
28.d	even	2	1		1008.3.f.a		1
84.h	odd	2	1		112.3.c.a		1
84.j	odd	6	2		784.3.s.a		2
84.n	even	6	2		784.3.s.a		2
105.g	even	2	1		175.3.d.a		1
105.k	odd	4	2		175.3.c.a		2
168.e	odd	2	1		448.3.c.b		1
168.i	even	2	1		448.3.c.a		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
7.3.b.a	✓	1	3.b	odd	2	1
7.3.b.a	✓	1	21.c	even	2	1
49.3.d.a		2	21.g	even	6	2
49.3.d.a		2	21.h	odd	6	2
63.3.d.a		1	1.a	even	1	1	trivial
63.3.d.a		1	7.b	odd	2	1	CM
112.3.c.a		1	12.b	even	2	1
112.3.c.a		1	84.h	odd	2	1
175.3.c.a		2	15.e	even	4	2
175.3.c.a		2	105.k	odd	4	2
175.3.d.a		1	15.d	odd	2	1
175.3.d.a		1	105.g	even	2	1
441.3.m.a		2	7.c	even	3	2
441.3.m.a		2	7.d	odd	6	2
448.3.c.a		1	24.h	odd	2	1
448.3.c.a		1	168.i	even	2	1
448.3.c.b		1	24.f	even	2	1
448.3.c.b		1	168.e	odd	2	1
784.3.s.a		2	84.j	odd	6	2
784.3.s.a		2	84.n	even	6	2
1008.3.f.a		1	4.b	odd	2	1
1008.3.f.a		1	28.d	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 3 \) acting on \(S_{3}^{\mathrm{new}}(63, [\chi])\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T - 3 \)
$3$	\( T \)
$5$	\( T \)
$7$	\( T + 7 \)
$11$	\( T - 6 \)