Newform orbit 2695.1.g.g

• Label: 2695.1.g.g
• Level: $2695$
• Weight: $1$
• Character orbit: 2695.g
• Self dual: yes
• Analytic conductor: $1.345$
• Analytic rank: $0$
• Dimension: $2$
• Projective image: $D_{6}$
• CM discriminant: -55
• 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:	\(2\)
Coefficient field:	\(\Q(\sqrt{3}) \)
Defining polynomial:	\( x^{2} - 3 \)
Coefficient ring:	\(\Z[a_1, a_2]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 385)
Projective image:	\(D_{6}\)
Projective field:	Galois closure of 6.0.79893275.1

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{3}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q - \beta q^{2} + 2 q^{4} - q^{5} - \beta q^{8} + q^{9} +O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{4} - 2 q^{5} + 2 q^{9}+O(q^{10}) \)

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

1.73205
−1.73205

−1.73205

0

2.00000

−1.00000

0

0

−1.73205

1.00000

1.73205

1814.2

1.73205

0

2.00000

−1.00000

0

0

1.73205

1.00000

−1.73205

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2695.1.g.g		2
5.b	even	2	1	inner	2695.1.g.g		2
7.b	odd	2	1		2695.1.g.h		2
7.c	even	3	2		385.1.q.c	✓	4
7.d	odd	6	2		2695.1.q.e		4
11.b	odd	2	1	inner	2695.1.g.g		2
21.h	odd	6	2		3465.1.cd.c		4
35.c	odd	2	1		2695.1.g.h		2
35.i	odd	6	2		2695.1.q.e		4
35.j	even	6	2		385.1.q.c	✓	4
35.l	odd	12	2		1925.1.w.a		2
35.l	odd	12	2		1925.1.w.b		2
55.d	odd	2	1	CM	2695.1.g.g		2
77.b	even	2	1		2695.1.g.h		2
77.h	odd	6	2		385.1.q.c	✓	4
77.i	even	6	2		2695.1.q.e		4
105.o	odd	6	2		3465.1.cd.c		4
231.l	even	6	2		3465.1.cd.c		4
385.h	even	2	1		2695.1.g.h		2
385.o	even	6	2		2695.1.q.e		4
385.q	odd	6	2		385.1.q.c	✓	4
385.bc	even	12	2		1925.1.w.a		2
385.bc	even	12	2		1925.1.w.b		2
1155.bo	even	6	2		3465.1.cd.c		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
385.1.q.c	✓	4	7.c	even	3	2
385.1.q.c	✓	4	35.j	even	6	2
385.1.q.c	✓	4	77.h	odd	6	2
385.1.q.c	✓	4	385.q	odd	6	2
1925.1.w.a		2	35.l	odd	12	2
1925.1.w.a		2	385.bc	even	12	2
1925.1.w.b		2	35.l	odd	12	2
1925.1.w.b		2	385.bc	even	12	2
2695.1.g.g		2	1.a	even	1	1	trivial
2695.1.g.g		2	5.b	even	2	1	inner
2695.1.g.g		2	11.b	odd	2	1	inner
2695.1.g.g		2	55.d	odd	2	1	CM
2695.1.g.h		2	7.b	odd	2	1
2695.1.g.h		2	35.c	odd	2	1
2695.1.g.h		2	77.b	even	2	1
2695.1.g.h		2	385.h	even	2	1
2695.1.q.e		4	7.d	odd	6	2
2695.1.q.e		4	35.i	odd	6	2
2695.1.q.e		4	77.i	even	6	2
2695.1.q.e		4	385.o	even	6	2
3465.1.cd.c		4	21.h	odd	6	2
3465.1.cd.c		4	105.o	odd	6	2
3465.1.cd.c		4	231.l	even	6	2
3465.1.cd.c		4	1155.bo	even	6	2

Hecke kernels

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

\( T_{2}^{2} - 3 \)

\( T_{3} \)

\( T_{13}^{2} - 3 \)

\( T_{31} - 1 \)

Hecke characteristic polynomials

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