Newform orbit 1444.2.a.b

• Label: 1444.2.a.b
• Level: $1444$
• Weight: $2$
• Character orbit: 1444.a
• Self dual: yes
• Analytic conductor: $11.530$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1444 = 2^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1444.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(11.5303980519\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 76)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

\( q - q^{3} - q^{5} - 2 q^{9}+O(q^{10}) \)

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

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1.1

0

0

−1.00000

0

−1.00000

0

0

0

−2.00000

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\(-1\)
\(19\)	\(1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1444.2.a.b		1
4.b	odd	2	1		5776.2.a.k		1
19.b	odd	2	1		1444.2.a.c		1
19.c	even	3	2		76.2.e.a	✓	2
19.d	odd	6	2		1444.2.e.b		2
57.h	odd	6	2		684.2.k.b		2
76.d	even	2	1		5776.2.a.f		1
76.g	odd	6	2		304.2.i.a		2
95.i	even	6	2		1900.2.i.a		2
95.m	odd	12	4		1900.2.s.a		4
152.k	odd	6	2		1216.2.i.g		2
152.p	even	6	2		1216.2.i.c		2
228.m	even	6	2		2736.2.s.g		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
76.2.e.a	✓	2	19.c	even	3	2
304.2.i.a		2	76.g	odd	6	2
684.2.k.b		2	57.h	odd	6	2
1216.2.i.c		2	152.p	even	6	2
1216.2.i.g		2	152.k	odd	6	2
1444.2.a.b		1	1.a	even	1	1	trivial
1444.2.a.c		1	19.b	odd	2	1
1444.2.e.b		2	19.d	odd	6	2
1900.2.i.a		2	95.i	even	6	2
1900.2.s.a		4	95.m	odd	12	4
2736.2.s.g		2	228.m	even	6	2
5776.2.a.f		1	76.d	even	2	1
5776.2.a.k		1	4.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} + 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1444))\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T \)
$3$	\( T + 1 \)
$5$	\( T + 1 \)
$7$	\( T \)
$11$	\( T + 4 \)