Newform orbit 1521.2.a.c

• Label: 1521.2.a.c
• Level: $1521$
• Weight: $2$
• Character orbit: 1521.a
• Self dual: yes
• Analytic conductor: $12.145$
• Analytic rank: $1$
• Dimension: $1$
• CM discriminant: -3
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1521 = 3^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1521.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(12.1452461474\)
Analytic rank:	\(1\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 117)
Fricke sign:	\(1\)
Sato-Tate group:	$N(\mathrm{U}(1))$

$q$-expansion

\(f(q)\)

\(=\)

\( q - 2 q^{4} + q^{7}+O(q^{10}) \)

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

0

−2.00000

0

0

1.00000

0

0

0

Atkin-Lehner signs

\( p \)	Sign
\(3\)	\(1\)
\(13\)	\(1\)

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1521.2.a.c		1
3.b	odd	2	1	CM	1521.2.a.c		1
13.b	even	2	1		1521.2.a.b		1
13.d	odd	4	2		1521.2.b.e		2
13.e	even	6	2		117.2.g.a	✓	2
39.d	odd	2	1		1521.2.a.b		1
39.f	even	4	2		1521.2.b.e		2
39.h	odd	6	2		117.2.g.a	✓	2
52.i	odd	6	2		1872.2.t.g		2
156.r	even	6	2		1872.2.t.g		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
117.2.g.a	✓	2	13.e	even	6	2
117.2.g.a	✓	2	39.h	odd	6	2
1521.2.a.b		1	13.b	even	2	1
1521.2.a.b		1	39.d	odd	2	1
1521.2.a.c		1	1.a	even	1	1	trivial
1521.2.a.c		1	3.b	odd	2	1	CM
1521.2.b.e		2	13.d	odd	4	2
1521.2.b.e		2	39.f	even	4	2
1872.2.t.g		2	52.i	odd	6	2
1872.2.t.g		2	156.r	even	6	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1521))\):

\( T_{2} \)

\( T_{5} \)

\( T_{7} - 1 \)

Hecke characteristic polynomials

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