Newform orbit 2700.1.g.b

• Label: 2700.1.g.b
• Level: $2700$
• Weight: $1$
• Character orbit: 2700.g
• Self dual: yes
• Analytic conductor: $1.347$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -3
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$2700 = 2^{2} \cdot 3^{3} \cdot 5^{2}$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	2700.g (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$1.34747553411$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 108)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.108.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.2.1458000.2
Stark unit:	Root of $x^{6} - 21066x^{5} + 5624655x^{4} - 432569180x^{3} + 5624655x^{2} - 21066x + 1$

$q$-expansion

$f(q)$

$=$

$q + q^{7} + q^{13} - q^{19} + 2 q^{31} + q^{37} - 2 q^{43} - q^{61} + q^{67} + q^{73} - q^{79} + q^{91} + q^{97}+O(q^{100})$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2700\mathbb{Z}\right)^\times$.

$n$	$1001$	$1351$	$2377$
$\chi(n)$	$-1$	$1$	$1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

701.1

0

0

0

0

0

0

1.00000

0

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	CM by $\Q(\sqrt{-3})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2700.1.g.b		1
3.b	odd	2	1	CM	2700.1.g.b		1
5.b	even	2	1		108.1.c.a	✓	1
5.c	odd	4	2		2700.1.b.b		2
15.d	odd	2	1		108.1.c.a	✓	1
15.e	even	4	2		2700.1.b.b		2
20.d	odd	2	1		432.1.e.a		1
40.e	odd	2	1		1728.1.e.b		1
40.f	even	2	1		1728.1.e.a		1
45.h	odd	6	2		324.1.g.a		2
45.j	even	6	2		324.1.g.a		2
60.h	even	2	1		432.1.e.a		1
120.i	odd	2	1		1728.1.e.a		1
120.m	even	2	1		1728.1.e.b		1
135.n	odd	18	6		2916.1.k.c		6
135.p	even	18	6		2916.1.k.c		6
180.n	even	6	2		1296.1.q.a		2
180.p	odd	6	2		1296.1.q.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
108.1.c.a	✓	1	5.b	even	2	1
108.1.c.a	✓	1	15.d	odd	2	1
324.1.g.a		2	45.h	odd	6	2
324.1.g.a		2	45.j	even	6	2
432.1.e.a		1	20.d	odd	2	1
432.1.e.a		1	60.h	even	2	1
1296.1.q.a		2	180.n	even	6	2
1296.1.q.a		2	180.p	odd	6	2
1728.1.e.a		1	40.f	even	2	1
1728.1.e.a		1	120.i	odd	2	1
1728.1.e.b		1	40.e	odd	2	1
1728.1.e.b		1	120.m	even	2	1
2700.1.b.b		2	5.c	odd	4	2
2700.1.b.b		2	15.e	even	4	2
2700.1.g.b		1	1.a	even	1	1	trivial
2700.1.g.b		1	3.b	odd	2	1	CM
2916.1.k.c		6	135.n	odd	18	6
2916.1.k.c		6	135.p	even	18	6

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{7} - 1$ acting on $S_{1}^{\mathrm{new}}(2700, [\chi])$.

Hecke characteristic polynomials

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