Newform orbit 1815.1.g.h

• Label: 1815.1.g.h
• Level: $1815$
• Weight: $1$
• Character orbit: 1815.g
• Self dual: yes
• Analytic conductor: $0.906$
• Analytic rank: $0$
• Dimension: $2$
• Projective image: $D_{6}$
• CM discriminant: -15
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1815.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.905802997929\)
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:	yes
Projective image:	\(D_{6}\)
Projective field:	Galois closure of 6.0.36236475.1

$q$-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.

\(f(q)\)	\(=\)	\( q - \beta q^{2} + q^{3} + 2 q^{4} - q^{5} - \beta q^{6} - \beta q^{8} + q^{9} +O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times\).

\(n\)	\(727\)	\(1211\)	\(1696\)
\(\chi(n)\)	\(-1\)	\(-1\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1574.1

1.73205
−1.73205

−1.73205

1.00000

2.00000

−1.00000

−1.73205

0

−1.73205

1.00000

1.73205

1574.2

1.73205

1.00000

2.00000

−1.00000

1.73205

0

1.73205

1.00000

−1.73205

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
15.d	odd	2	1	CM by \(\Q(\sqrt{-15}) \)
11.b	odd	2	1	inner
165.d	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1815.1.g.h	yes	2
3.b	odd	2	1		1815.1.g.g	✓	2
5.b	even	2	1		1815.1.g.g	✓	2
11.b	odd	2	1	inner	1815.1.g.h	yes	2
11.c	even	5	4		1815.1.o.g		8
11.d	odd	10	4		1815.1.o.g		8
15.d	odd	2	1	CM	1815.1.g.h	yes	2
33.d	even	2	1		1815.1.g.g	✓	2
33.f	even	10	4		1815.1.o.h		8
33.h	odd	10	4		1815.1.o.h		8
55.d	odd	2	1		1815.1.g.g	✓	2
55.h	odd	10	4		1815.1.o.h		8
55.j	even	10	4		1815.1.o.h		8
165.d	even	2	1	inner	1815.1.g.h	yes	2
165.o	odd	10	4		1815.1.o.g		8
165.r	even	10	4		1815.1.o.g		8

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1815.1.g.g	✓	2	3.b	odd	2	1
1815.1.g.g	✓	2	5.b	even	2	1
1815.1.g.g	✓	2	33.d	even	2	1
1815.1.g.g	✓	2	55.d	odd	2	1
1815.1.g.h	yes	2	1.a	even	1	1	trivial
1815.1.g.h	yes	2	11.b	odd	2	1	inner
1815.1.g.h	yes	2	15.d	odd	2	1	CM
1815.1.g.h	yes	2	165.d	even	2	1	inner
1815.1.o.g		8	11.c	even	5	4
1815.1.o.g		8	11.d	odd	10	4
1815.1.o.g		8	165.o	odd	10	4
1815.1.o.g		8	165.r	even	10	4
1815.1.o.h		8	33.f	even	10	4
1815.1.o.h		8	33.h	odd	10	4
1815.1.o.h		8	55.h	odd	10	4
1815.1.o.h		8	55.j	even	10	4

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(1815, [\chi])\):

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

\( T_{19} \)

\( T_{23} + 1 \)

Hecke characteristic polynomials

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