Newform orbit 2835.1.e.a

• Label: 2835.1.e.a
• Level: $2835$
• Weight: $1$
• Character orbit: 2835.e
• Self dual: yes
• Analytic conductor: $1.415$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -35
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2835 = 3^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2835.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(1.41484931081\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 315)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.2835.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.2.40186125.1
Stark unit:	Root of $x^{6} - 8133x^{5} - 1061706x^{4} - 68285369x^{3} - 1061706x^{2} - 8133x + 1$

$q$-expansion

\(f(q)\)

\(=\)

q + q^4 - q^5 - q^7 - q^11 + q^13 + q^16 + q^17 - q^20 + q^25 - q^28 + 2 * q^29 + q^35 - q^44 + q^47 + q^49 + q^52 + q^55 + q^64 - q^65 + q^68 - q^71 + q^73 + q^77 - q^79 - q^80 + q^83 - q^85 - q^91 + q^97

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2835\mathbb{Z}\right)^\times\).

\(n\)	\(1541\)	\(1702\)	\(2026\)
\(\chi(n)\)	\(0\)	\(1\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

244.1

0

0

0

1.00000

−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	2835.1.e.a		1
3.b	odd	2	1		2835.1.e.c		1
5.b	even	2	1		2835.1.e.d		1
7.b	odd	2	1		2835.1.e.d		1
9.c	even	3	2		315.1.bg.a	✓	2
9.d	odd	6	2		945.1.bg.a		2
15.d	odd	2	1		2835.1.e.b		1
21.c	even	2	1		2835.1.e.b		1
35.c	odd	2	1	CM	2835.1.e.a		1
45.h	odd	6	2		945.1.bg.b		2
45.j	even	6	2		315.1.bg.b	yes	2
45.k	odd	12	4		1575.1.y.a		4
63.g	even	3	2		2205.1.bn.b		2
63.h	even	3	2		2205.1.q.b		2
63.k	odd	6	2		2205.1.bn.a		2
63.l	odd	6	2		315.1.bg.b	yes	2
63.o	even	6	2		945.1.bg.b		2
63.t	odd	6	2		2205.1.q.a		2
105.g	even	2	1		2835.1.e.c		1
315.q	odd	6	2		2205.1.q.b		2
315.r	even	6	2		2205.1.q.a		2
315.z	even	6	2		945.1.bg.a		2
315.bg	odd	6	2		315.1.bg.a	✓	2
315.bn	odd	6	2		2205.1.bn.b		2
315.bo	even	6	2		2205.1.bn.a		2
315.cb	even	12	4		1575.1.y.a		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
315.1.bg.a	✓	2	9.c	even	3	2
315.1.bg.a	✓	2	315.bg	odd	6	2
315.1.bg.b	yes	2	45.j	even	6	2
315.1.bg.b	yes	2	63.l	odd	6	2
945.1.bg.a		2	9.d	odd	6	2
945.1.bg.a		2	315.z	even	6	2
945.1.bg.b		2	45.h	odd	6	2
945.1.bg.b		2	63.o	even	6	2
1575.1.y.a		4	45.k	odd	12	4
1575.1.y.a		4	315.cb	even	12	4
2205.1.q.a		2	63.t	odd	6	2
2205.1.q.a		2	315.r	even	6	2
2205.1.q.b		2	63.h	even	3	2
2205.1.q.b		2	315.q	odd	6	2
2205.1.bn.a		2	63.k	odd	6	2
2205.1.bn.a		2	315.bo	even	6	2
2205.1.bn.b		2	63.g	even	3	2
2205.1.bn.b		2	315.bn	odd	6	2
2835.1.e.a		1	1.a	even	1	1	trivial
2835.1.e.a		1	35.c	odd	2	1	CM
2835.1.e.b		1	15.d	odd	2	1
2835.1.e.b		1	21.c	even	2	1
2835.1.e.c		1	3.b	odd	2	1
2835.1.e.c		1	105.g	even	2	1
2835.1.e.d		1	5.b	even	2	1
2835.1.e.d		1	7.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(2835, [\chi])\):

\( T_{11} + 1 \)

\( T_{13} - 1 \)

Hecke characteristic polynomials

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