Newform orbit 1805.1.h.a

• Label: 1805.1.h.a
• Level: $1805$
• Weight: $1$
• Character orbit: 1805.h
• Analytic conductor: $0.901$
• Analytic rank: $0$
• Dimension: $2$
• Projective image: $D_{2}$
• CM/RM discs: -19, -95, 5
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1805.h (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.900812347803\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\zeta_{6})\)
Defining polynomial:	\( x^{2} - x + 1 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 95)
Projective image:	\(D_{2}\)
Projective field:	Galois closure of \(\Q(\sqrt{5}, \sqrt{-19})\)
Artin image:	$C_3\times D_4$
Artin field:	Galois closure of \(\mathbb{Q}[x]/(x^{12} - \cdots)\)

$q$-expansion

The \(q\)-expansion and trace form are shown below.

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).

\(n\)	\(362\)	\(1446\)
\(\chi(n)\)	\(-1\)	\(\zeta_{6}\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

69.1

0.500000	−	0.866025i
0.500000	+	0.866025i

0

0

0.500000

−

0.866025i

−0.500000

−

0.866025i

0

0

0

0.500000

−

0.866025i

0

654.1

0

0

0.500000

+

0.866025i

−0.500000

+

0.866025i

0

0

0

0.500000

+

0.866025i

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	RM by \(\Q(\sqrt{5}) \)
19.b	odd	2	1	CM by \(\Q(\sqrt{-19}) \)
95.d	odd	2	1	CM by \(\Q(\sqrt{-95}) \)
19.c	even	3	1	inner
19.d	odd	6	1	inner
95.h	odd	6	1	inner
95.i	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1805.1.h.a		2
5.b	even	2	1	RM	1805.1.h.a		2
19.b	odd	2	1	CM	1805.1.h.a		2
19.c	even	3	1		95.1.d.a	✓	1
19.c	even	3	1	inner	1805.1.h.a		2
19.d	odd	6	1		95.1.d.a	✓	1
19.d	odd	6	1	inner	1805.1.h.a		2
19.e	even	9	6		1805.1.o.a		6
19.f	odd	18	6		1805.1.o.a		6
57.f	even	6	1		855.1.g.a		1
57.h	odd	6	1		855.1.g.a		1
76.f	even	6	1		1520.1.m.a		1
76.g	odd	6	1		1520.1.m.a		1
95.d	odd	2	1	CM	1805.1.h.a		2
95.h	odd	6	1		95.1.d.a	✓	1
95.h	odd	6	1	inner	1805.1.h.a		2
95.i	even	6	1		95.1.d.a	✓	1
95.i	even	6	1	inner	1805.1.h.a		2
95.l	even	12	2		475.1.c.a		1
95.m	odd	12	2		475.1.c.a		1
95.o	odd	18	6		1805.1.o.a		6
95.p	even	18	6		1805.1.o.a		6
285.n	odd	6	1		855.1.g.a		1
285.q	even	6	1		855.1.g.a		1
380.p	odd	6	1		1520.1.m.a		1
380.s	even	6	1		1520.1.m.a		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.1.d.a	✓	1	19.c	even	3	1
95.1.d.a	✓	1	19.d	odd	6	1
95.1.d.a	✓	1	95.h	odd	6	1
95.1.d.a	✓	1	95.i	even	6	1
475.1.c.a		1	95.l	even	12	2
475.1.c.a		1	95.m	odd	12	2
855.1.g.a		1	57.f	even	6	1
855.1.g.a		1	57.h	odd	6	1
855.1.g.a		1	285.n	odd	6	1
855.1.g.a		1	285.q	even	6	1
1520.1.m.a		1	76.f	even	6	1
1520.1.m.a		1	76.g	odd	6	1
1520.1.m.a		1	380.p	odd	6	1
1520.1.m.a		1	380.s	even	6	1
1805.1.h.a		2	1.a	even	1	1	trivial
1805.1.h.a		2	5.b	even	2	1	RM
1805.1.h.a		2	19.b	odd	2	1	CM
1805.1.h.a		2	19.c	even	3	1	inner
1805.1.h.a		2	19.d	odd	6	1	inner
1805.1.h.a		2	95.d	odd	2	1	CM
1805.1.h.a		2	95.h	odd	6	1	inner
1805.1.h.a		2	95.i	even	6	1	inner
1805.1.o.a		6	19.e	even	9	6
1805.1.o.a		6	19.f	odd	18	6
1805.1.o.a		6	95.o	odd	18	6
1805.1.o.a		6	95.p	even	18	6

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} \) acting on \(S_{1}^{\mathrm{new}}(1805, [\chi])\).

Hecke characteristic polynomials

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