Newform orbit 2695.1.g.c

• Label: 2695.1.g.c
• Level: $2695$
• Weight: $1$
• Character orbit: 2695.g
• Self dual: yes
• Analytic conductor: $1.345$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{2}$
• CM/RM discs: -11, -55, 5
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2695.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(1.34498020905\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 55)
Projective image:	\(D_{2}\)
Projective field:	Galois closure of \(\Q(\sqrt{5}, \sqrt{-11})\)
Artin image:	$D_4$
Artin field:	Galois closure of 4.2.13475.1
Stark unit:	Root of $x^{4} - 6339x^{3} - 799x^{2} - 6339x + 1$

$q$-expansion

\(f(q)\)

\(=\)

\( q - q^{4} + q^{5} + q^{9} - q^{11} + q^{16} - q^{20} + q^{25} + 2 q^{31} - q^{36} + q^{44} + q^{45} - q^{55} - 2 q^{59} - q^{64} + 2 q^{71} + q^{80} + q^{81} + 2 q^{89} - q^{99}+O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2695\mathbb{Z}\right)^\times\).

\(n\)	\(981\)	\(1816\)	\(2157\)
\(\chi(n)\)	\(-1\)	\(1\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1814.1

0

0

0

−1.00000

1.00000

0

0

0

1.00000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	RM by \(\Q(\sqrt{5}) \)
11.b	odd	2	1	CM by \(\Q(\sqrt{-11}) \)
55.d	odd	2	1	CM by \(\Q(\sqrt{-55}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2695.1.g.c		1
5.b	even	2	1	RM	2695.1.g.c		1
7.b	odd	2	1		55.1.d.a	✓	1
7.c	even	3	2		2695.1.q.b		2
7.d	odd	6	2		2695.1.q.c		2
11.b	odd	2	1	CM	2695.1.g.c		1
21.c	even	2	1		495.1.h.a		1
28.d	even	2	1		880.1.i.a		1
35.c	odd	2	1		55.1.d.a	✓	1
35.f	even	4	2		275.1.c.a		1
35.i	odd	6	2		2695.1.q.c		2
35.j	even	6	2		2695.1.q.b		2
55.d	odd	2	1	CM	2695.1.g.c		1
56.e	even	2	1		3520.1.i.a		1
56.h	odd	2	1		3520.1.i.b		1
77.b	even	2	1		55.1.d.a	✓	1
77.h	odd	6	2		2695.1.q.b		2
77.i	even	6	2		2695.1.q.c		2
77.j	odd	10	4		605.1.h.a		4
77.l	even	10	4		605.1.h.a		4
105.g	even	2	1		495.1.h.a		1
105.k	odd	4	2		2475.1.b.a		1
140.c	even	2	1		880.1.i.a		1
231.h	odd	2	1		495.1.h.a		1
280.c	odd	2	1		3520.1.i.b		1
280.n	even	2	1		3520.1.i.a		1
308.g	odd	2	1		880.1.i.a		1
385.h	even	2	1		55.1.d.a	✓	1
385.l	odd	4	2		275.1.c.a		1
385.o	even	6	2		2695.1.q.c		2
385.q	odd	6	2		2695.1.q.b		2
385.v	even	10	4		605.1.h.a		4
385.y	odd	10	4		605.1.h.a		4
385.bi	odd	20	8		3025.1.x.a		4
385.bk	even	20	8		3025.1.x.a		4
616.g	odd	2	1		3520.1.i.a		1
616.o	even	2	1		3520.1.i.b		1
1155.e	odd	2	1		495.1.h.a		1
1155.t	even	4	2		2475.1.b.a		1
1540.b	odd	2	1		880.1.i.a		1
3080.k	even	2	1		3520.1.i.b		1
3080.bc	odd	2	1		3520.1.i.a		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
55.1.d.a	✓	1	7.b	odd	2	1
55.1.d.a	✓	1	35.c	odd	2	1
55.1.d.a	✓	1	77.b	even	2	1
55.1.d.a	✓	1	385.h	even	2	1
275.1.c.a		1	35.f	even	4	2
275.1.c.a		1	385.l	odd	4	2
495.1.h.a		1	21.c	even	2	1
495.1.h.a		1	105.g	even	2	1
495.1.h.a		1	231.h	odd	2	1
495.1.h.a		1	1155.e	odd	2	1
605.1.h.a		4	77.j	odd	10	4
605.1.h.a		4	77.l	even	10	4
605.1.h.a		4	385.v	even	10	4
605.1.h.a		4	385.y	odd	10	4
880.1.i.a		1	28.d	even	2	1
880.1.i.a		1	140.c	even	2	1
880.1.i.a		1	308.g	odd	2	1
880.1.i.a		1	1540.b	odd	2	1
2475.1.b.a		1	105.k	odd	4	2
2475.1.b.a		1	1155.t	even	4	2
2695.1.g.c		1	1.a	even	1	1	trivial
2695.1.g.c		1	5.b	even	2	1	RM
2695.1.g.c		1	11.b	odd	2	1	CM
2695.1.g.c		1	55.d	odd	2	1	CM
2695.1.q.b		2	7.c	even	3	2
2695.1.q.b		2	35.j	even	6	2
2695.1.q.b		2	77.h	odd	6	2
2695.1.q.b		2	385.q	odd	6	2
2695.1.q.c		2	7.d	odd	6	2
2695.1.q.c		2	35.i	odd	6	2
2695.1.q.c		2	77.i	even	6	2
2695.1.q.c		2	385.o	even	6	2
3025.1.x.a		4	385.bi	odd	20	8
3025.1.x.a		4	385.bk	even	20	8
3520.1.i.a		1	56.e	even	2	1
3520.1.i.a		1	280.n	even	2	1
3520.1.i.a		1	616.g	odd	2	1
3520.1.i.a		1	3080.bc	odd	2	1
3520.1.i.b		1	56.h	odd	2	1
3520.1.i.b		1	280.c	odd	2	1
3520.1.i.b		1	616.o	even	2	1
3520.1.i.b		1	3080.k	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(2695, [\chi])\):

\( T_{2} \)

\( T_{3} \)

\( T_{13} \)

\( T_{31} - 2 \)

Hecke characteristic polynomials

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