Newform orbit 1805.1.o.a

• Label: 1805.1.o.a
• Level: $1805$
• Weight: $1$
• Character orbit: 1805.o
• Analytic conductor: $0.901$
• Analytic rank: $0$
• Dimension: $6$
• Projective image: $D_{2}$
• CM/RM discs: -19, -95, 5
• Inner twists: $24$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1805.o (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.900812347803\)
Analytic rank:	\(0\)
Dimension:	\(6\)
Coefficient field:	\(\Q(\zeta_{18})\)
Defining polynomial:	\( x^{6} - x^{3} + 1 \)
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:	$C_9\times D_4$
Artin field:	Galois closure of \(\mathbb{Q}[x]/(x^{36} - \cdots)\)

$q$-expansion

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

\(f(q)\)	\(=\)	\( q - \zeta_{18}^{2} q^{4} - \zeta_{18}^{7} q^{5} - \zeta_{18}^{8} q^{9} +O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q+O(q^{10}) \)

Character values

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

\(n\)	\(362\)	\(1446\)
\(\chi(n)\)	\(-1\)	\(-\zeta_{18}^{2}\)

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

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

299.1

0.939693	−	0.342020i
−0.173648	−	0.984808i
−0.766044	+	0.642788i
0.939693	+	0.342020i
−0.766044	−	0.642788i
−0.173648	+	0.984808i

0

0

−0.766044

+

0.642788i

0.766044

+

0.642788i

0

0

0

0.939693

+

0.342020i

0

694.1

0

0

0.939693

−

0.342020i

−0.939693

−

0.342020i

0

0

0

−0.173648

+

0.984808i

0

849.1

0

0

−0.173648

+

0.984808i

0.173648

+

0.984808i

0

0

0

−0.766044

−

0.642788i

0

984.1

0

0

−0.766044

−

0.642788i

0.766044

−

0.642788i

0

0

0

0.939693

−

0.342020i

0

1029.1

0

0

−0.173648

−

0.984808i

0.173648

−

0.984808i

0

0

0

−0.766044

+

0.642788i

0

1199.1

0

0

0.939693

+

0.342020i

−0.939693

+

0.342020i

0

0

0

−0.173648

−

0.984808i

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	2	inner
19.d	odd	6	2	inner
19.e	even	9	3	inner
19.f	odd	18	3	inner
95.h	odd	6	2	inner
95.i	even	6	2	inner
95.o	odd	18	3	inner
95.p	even	18	3	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1805.1.o.a		6
5.b	even	2	1	RM	1805.1.o.a		6
19.b	odd	2	1	CM	1805.1.o.a		6
19.c	even	3	2	inner	1805.1.o.a		6
19.d	odd	6	2	inner	1805.1.o.a		6
19.e	even	9	1		95.1.d.a	✓	1
19.e	even	9	2		1805.1.h.a		2
19.e	even	9	3	inner	1805.1.o.a		6
19.f	odd	18	1		95.1.d.a	✓	1
19.f	odd	18	2		1805.1.h.a		2
19.f	odd	18	3	inner	1805.1.o.a		6
57.j	even	18	1		855.1.g.a		1
57.l	odd	18	1		855.1.g.a		1
76.k	even	18	1		1520.1.m.a		1
76.l	odd	18	1		1520.1.m.a		1
95.d	odd	2	1	CM	1805.1.o.a		6
95.h	odd	6	2	inner	1805.1.o.a		6
95.i	even	6	2	inner	1805.1.o.a		6
95.o	odd	18	1		95.1.d.a	✓	1
95.o	odd	18	2		1805.1.h.a		2
95.o	odd	18	3	inner	1805.1.o.a		6
95.p	even	18	1		95.1.d.a	✓	1
95.p	even	18	2		1805.1.h.a		2
95.p	even	18	3	inner	1805.1.o.a		6
95.q	odd	36	2		475.1.c.a		1
95.r	even	36	2		475.1.c.a		1
285.bd	odd	18	1		855.1.g.a		1
285.bf	even	18	1		855.1.g.a		1
380.ba	odd	18	1		1520.1.m.a		1
380.bb	even	18	1		1520.1.m.a		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.1.d.a	✓	1	19.e	even	9	1
95.1.d.a	✓	1	19.f	odd	18	1
95.1.d.a	✓	1	95.o	odd	18	1
95.1.d.a	✓	1	95.p	even	18	1
475.1.c.a		1	95.q	odd	36	2
475.1.c.a		1	95.r	even	36	2
855.1.g.a		1	57.j	even	18	1
855.1.g.a		1	57.l	odd	18	1
855.1.g.a		1	285.bd	odd	18	1
855.1.g.a		1	285.bf	even	18	1
1520.1.m.a		1	76.k	even	18	1
1520.1.m.a		1	76.l	odd	18	1
1520.1.m.a		1	380.ba	odd	18	1
1520.1.m.a		1	380.bb	even	18	1
1805.1.h.a		2	19.e	even	9	2
1805.1.h.a		2	19.f	odd	18	2
1805.1.h.a		2	95.o	odd	18	2
1805.1.h.a		2	95.p	even	18	2
1805.1.o.a		6	1.a	even	1	1	trivial
1805.1.o.a		6	5.b	even	2	1	RM
1805.1.o.a		6	19.b	odd	2	1	CM
1805.1.o.a		6	19.c	even	3	2	inner
1805.1.o.a		6	19.d	odd	6	2	inner
1805.1.o.a		6	19.e	even	9	3	inner
1805.1.o.a		6	19.f	odd	18	3	inner
1805.1.o.a		6	95.d	odd	2	1	CM
1805.1.o.a		6	95.h	odd	6	2	inner
1805.1.o.a		6	95.i	even	6	2	inner
1805.1.o.a		6	95.o	odd	18	3	inner
1805.1.o.a		6	95.p	even	18	3	inner

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

$p$	$F_p(T)$
$2$	\( T^{6} \)
$3$	\( T^{6} \)
$5$	\( T^{6} + T^{3} + 1 \)
$7$	\( T^{6} \)
$11$	\( (T^{2} - 2 T + 4)^{3} \)