Newform orbit 5929.2.a.c

• Label: 5929.2.a.c
• Level: $5929$
• Weight: $2$
• Character orbit: 5929.a
• Self dual: yes
• Analytic conductor: $47.343$
• Analytic rank: $1$
• Dimension: $1$
• CM discriminant: -7
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(47.3433033584\)
Analytic rank:	\(1\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 49)
Fricke sign:	\(1\)
Sato-Tate group:	$N(\mathrm{U}(1))$

$q$-expansion

\(f(q)\)

\(=\)

\( q - q^{2} - q^{4} + 3 q^{8} - 3 q^{9}+O(q^{10}) \)

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

−1.00000

0

−1.00000

0

0

0

3.00000

−3.00000

0

Atkin-Lehner signs

\( p \)	Sign
\(7\)	\(-1\)
\(11\)	\(-1\)

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	CM by \(\Q(\sqrt{-7}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	5929.2.a.c		1
7.b	odd	2	1	CM	5929.2.a.c		1
11.b	odd	2	1		49.2.a.a	✓	1
33.d	even	2	1		441.2.a.c		1
44.c	even	2	1		784.2.a.f		1
55.d	odd	2	1		1225.2.a.c		1
55.e	even	4	2		1225.2.b.c		2
77.b	even	2	1		49.2.a.a	✓	1
77.h	odd	6	2		49.2.c.a		2
77.i	even	6	2		49.2.c.a		2
88.b	odd	2	1		3136.2.a.n		1
88.g	even	2	1		3136.2.a.o		1
132.d	odd	2	1		7056.2.a.bg		1
143.d	odd	2	1		8281.2.a.d		1
231.h	odd	2	1		441.2.a.c		1
231.k	odd	6	2		441.2.e.d		2
231.l	even	6	2		441.2.e.d		2
308.g	odd	2	1		784.2.a.f		1
308.m	odd	6	2		784.2.i.f		2
308.n	even	6	2		784.2.i.f		2
385.h	even	2	1		1225.2.a.c		1
385.l	odd	4	2		1225.2.b.c		2
616.g	odd	2	1		3136.2.a.o		1
616.o	even	2	1		3136.2.a.n		1
924.n	even	2	1		7056.2.a.bg		1
1001.g	even	2	1		8281.2.a.d		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
49.2.a.a	✓	1	11.b	odd	2	1
49.2.a.a	✓	1	77.b	even	2	1
49.2.c.a		2	77.h	odd	6	2
49.2.c.a		2	77.i	even	6	2
441.2.a.c		1	33.d	even	2	1
441.2.a.c		1	231.h	odd	2	1
441.2.e.d		2	231.k	odd	6	2
441.2.e.d		2	231.l	even	6	2
784.2.a.f		1	44.c	even	2	1
784.2.a.f		1	308.g	odd	2	1
784.2.i.f		2	308.m	odd	6	2
784.2.i.f		2	308.n	even	6	2
1225.2.a.c		1	55.d	odd	2	1
1225.2.a.c		1	385.h	even	2	1
1225.2.b.c		2	55.e	even	4	2
1225.2.b.c		2	385.l	odd	4	2
3136.2.a.n		1	88.b	odd	2	1
3136.2.a.n		1	616.o	even	2	1
3136.2.a.o		1	88.g	even	2	1
3136.2.a.o		1	616.g	odd	2	1
5929.2.a.c		1	1.a	even	1	1	trivial
5929.2.a.c		1	7.b	odd	2	1	CM
7056.2.a.bg		1	132.d	odd	2	1
7056.2.a.bg		1	924.n	even	2	1
8281.2.a.d		1	143.d	odd	2	1
8281.2.a.d		1	1001.g	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5929))\):

\( T_{2} + 1 \)

\( T_{3} \)

\( T_{5} \)

Hecke characteristic polynomials

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