Newform orbit 1444.1.h.a

• Label: 1444.1.h.a
• Level: $1444$
• Weight: $1$
• Character orbit: 1444.h
• Analytic conductor: $0.721$
• Analytic rank: $0$
• Dimension: $2$
• Projective image: $D_{3}$
• CM discriminant: -19
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1444 = 2^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1444.h (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.720649878242\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\zeta_{6})\)
Defining polynomial:	\( x^{2} - x + 1 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 76)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.76.1
Artin image:	$C_3\times S_3$
Artin field:	Galois closure of 6.0.39617584.1

$q$-expansion

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

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1444\mathbb{Z}\right)^\times\).

\(n\)	\(723\)	\(1085\)
\(\chi(n)\)	\(1\)	\(\zeta_{6}\)

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

0.500000

+

0.866025i

0

−1.00000

0

−0.500000

+

0.866025i

0

293.1

0

0

0

0.500000

−

0.866025i

0

−1.00000

0

−0.500000

−

0.866025i

0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1444.1.h.a		2
19.b	odd	2	1	CM	1444.1.h.a		2
19.c	even	3	1		76.1.c.a	✓	1
19.c	even	3	1	inner	1444.1.h.a		2
19.d	odd	6	1		76.1.c.a	✓	1
19.d	odd	6	1	inner	1444.1.h.a		2
19.e	even	9	6		1444.1.j.a		6
19.f	odd	18	6		1444.1.j.a		6
57.f	even	6	1		684.1.h.a		1
57.h	odd	6	1		684.1.h.a		1
76.f	even	6	1		304.1.e.a		1
76.g	odd	6	1		304.1.e.a		1
95.h	odd	6	1		1900.1.e.a		1
95.i	even	6	1		1900.1.e.a		1
95.l	even	12	2		1900.1.g.a		2
95.m	odd	12	2		1900.1.g.a		2
133.g	even	3	1		3724.1.bc.c		2
133.h	even	3	1		3724.1.bc.c		2
133.i	even	6	1		3724.1.bc.b		2
133.j	odd	6	1		3724.1.bc.c		2
133.k	odd	6	1		3724.1.bc.b		2
133.m	odd	6	1		3724.1.e.c		1
133.n	odd	6	1		3724.1.bc.c		2
133.p	even	6	1		3724.1.e.c		1
133.s	even	6	1		3724.1.bc.b		2
133.t	odd	6	1		3724.1.bc.b		2
152.k	odd	6	1		1216.1.e.b		1
152.l	odd	6	1		1216.1.e.a		1
152.o	even	6	1		1216.1.e.b		1
152.p	even	6	1		1216.1.e.a		1
228.m	even	6	1		2736.1.o.b		1
228.n	odd	6	1		2736.1.o.b		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
76.1.c.a	✓	1	19.c	even	3	1
76.1.c.a	✓	1	19.d	odd	6	1
304.1.e.a		1	76.f	even	6	1
304.1.e.a		1	76.g	odd	6	1
684.1.h.a		1	57.f	even	6	1
684.1.h.a		1	57.h	odd	6	1
1216.1.e.a		1	152.l	odd	6	1
1216.1.e.a		1	152.p	even	6	1
1216.1.e.b		1	152.k	odd	6	1
1216.1.e.b		1	152.o	even	6	1
1444.1.h.a		2	1.a	even	1	1	trivial
1444.1.h.a		2	19.b	odd	2	1	CM
1444.1.h.a		2	19.c	even	3	1	inner
1444.1.h.a		2	19.d	odd	6	1	inner
1444.1.j.a		6	19.e	even	9	6
1444.1.j.a		6	19.f	odd	18	6
1900.1.e.a		1	95.h	odd	6	1
1900.1.e.a		1	95.i	even	6	1
1900.1.g.a		2	95.l	even	12	2
1900.1.g.a		2	95.m	odd	12	2
2736.1.o.b		1	228.m	even	6	1
2736.1.o.b		1	228.n	odd	6	1
3724.1.e.c		1	133.m	odd	6	1
3724.1.e.c		1	133.p	even	6	1
3724.1.bc.b		2	133.i	even	6	1
3724.1.bc.b		2	133.k	odd	6	1
3724.1.bc.b		2	133.s	even	6	1
3724.1.bc.b		2	133.t	odd	6	1
3724.1.bc.c		2	133.g	even	3	1
3724.1.bc.c		2	133.h	even	3	1
3724.1.bc.c		2	133.j	odd	6	1
3724.1.bc.c		2	133.n	odd	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} \) acting on \(S_{1}^{\mathrm{new}}(1444, [\chi])\).

Hecke characteristic polynomials

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