Newform orbit 1260.1.p.a

• Label: 1260.1.p.a
• Level: $1260$
• Weight: $1$
• Character orbit: 1260.p
• Self dual: yes
• Analytic conductor: $0.629$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -35
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1260.p (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.628821915918\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 140)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.140.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.0.529200.1

$q$-expansion

\(f(q)\)

\(=\)

\( q - q^{5} + q^{7}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\)	\(281\)	\(631\)	\(757\)	\(1081\)
\(\chi(n)\)	\(1\)	\(1\)	\(-1\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1189.1

0

0

0

0

−1.00000

0

1.00000

0

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
35.c	odd	2	1	CM by \(\Q(\sqrt{-35}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1260.1.p.a		1
3.b	odd	2	1		140.1.h.a	✓	1
5.b	even	2	1		1260.1.p.b		1
7.b	odd	2	1		1260.1.p.b		1
12.b	even	2	1		560.1.p.b		1
15.d	odd	2	1		140.1.h.b	yes	1
15.e	even	4	2		700.1.d.a		2
21.c	even	2	1		140.1.h.b	yes	1
21.g	even	6	2		980.1.n.a		2
21.h	odd	6	2		980.1.n.b		2
24.f	even	2	1		2240.1.p.a		1
24.h	odd	2	1		2240.1.p.c		1
35.c	odd	2	1	CM	1260.1.p.a		1
60.h	even	2	1		560.1.p.a		1
60.l	odd	4	2		2800.1.f.c		2
84.h	odd	2	1		560.1.p.a		1
84.j	odd	6	2		3920.1.br.b		2
84.n	even	6	2		3920.1.br.a		2
105.g	even	2	1		140.1.h.a	✓	1
105.k	odd	4	2		700.1.d.a		2
105.o	odd	6	2		980.1.n.a		2
105.p	even	6	2		980.1.n.b		2
120.i	odd	2	1		2240.1.p.b		1
120.m	even	2	1		2240.1.p.d		1
168.e	odd	2	1		2240.1.p.d		1
168.i	even	2	1		2240.1.p.b		1
420.o	odd	2	1		560.1.p.b		1
420.w	even	4	2		2800.1.f.c		2
420.ba	even	6	2		3920.1.br.b		2
420.be	odd	6	2		3920.1.br.a		2
840.b	odd	2	1		2240.1.p.a		1
840.u	even	2	1		2240.1.p.c		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
140.1.h.a	✓	1	3.b	odd	2	1
140.1.h.a	✓	1	105.g	even	2	1
140.1.h.b	yes	1	15.d	odd	2	1
140.1.h.b	yes	1	21.c	even	2	1
560.1.p.a		1	60.h	even	2	1
560.1.p.a		1	84.h	odd	2	1
560.1.p.b		1	12.b	even	2	1
560.1.p.b		1	420.o	odd	2	1
700.1.d.a		2	15.e	even	4	2
700.1.d.a		2	105.k	odd	4	2
980.1.n.a		2	21.g	even	6	2
980.1.n.a		2	105.o	odd	6	2
980.1.n.b		2	21.h	odd	6	2
980.1.n.b		2	105.p	even	6	2
1260.1.p.a		1	1.a	even	1	1	trivial
1260.1.p.a		1	35.c	odd	2	1	CM
1260.1.p.b		1	5.b	even	2	1
1260.1.p.b		1	7.b	odd	2	1
2240.1.p.a		1	24.f	even	2	1
2240.1.p.a		1	840.b	odd	2	1
2240.1.p.b		1	120.i	odd	2	1
2240.1.p.b		1	168.i	even	2	1
2240.1.p.c		1	24.h	odd	2	1
2240.1.p.c		1	840.u	even	2	1
2240.1.p.d		1	120.m	even	2	1
2240.1.p.d		1	168.e	odd	2	1
2800.1.f.c		2	60.l	odd	4	2
2800.1.f.c		2	420.w	even	4	2
3920.1.br.a		2	84.n	even	6	2
3920.1.br.a		2	420.be	odd	6	2
3920.1.br.b		2	84.j	odd	6	2
3920.1.br.b		2	420.ba	even	6	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{13} + 1 \) acting on \(S_{1}^{\mathrm{new}}(1260, [\chi])\).

Hecke characteristic polynomials

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