Newform orbit 539.3.c.a

• Label: 539.3.c.a
• Level: $539$
• Weight: $3$
• Character orbit: 539.c
• Self dual: yes
• Analytic conductor: $14.687$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -11
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	539.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(14.6866862490\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\)

\(=\)

q + 5 * q^3 + 4 * q^4 + q^5 + 16 * q^9 - 11 * q^11 + 20 * q^12 + 5 * q^15 + 16 * q^16 + 4 * q^20 + 35 * q^23 - 24 * q^25 + 35 * q^27 + 37 * q^31 - 55 * q^33 + 64 * q^36 - 25 * q^37 - 44 * q^44 + 16 * q^45 - 50 * q^47 + 80 * q^48 - 70 * q^53 - 11 * q^55 - 107 * q^59 + 20 * q^60 + 64 * q^64 + 35 * q^67 + 175 * q^69 - 133 * q^71 - 120 * q^75 + 16 * q^80 + 31 * q^81 + 97 * q^89 + 140 * q^92 + 185 * q^93 - 95 * q^97 - 176 * q^99

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).

\(n\)	\(199\)	\(442\)
\(\chi(n)\)	\(1\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

197.1

0

0

5.00000

4.00000

1.00000

0

0

0

16.0000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.b	odd	2	1	CM by \(\Q(\sqrt{-11}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	539.3.c.a		1
7.b	odd	2	1		11.3.b.a	✓	1
11.b	odd	2	1	CM	539.3.c.a		1
21.c	even	2	1		99.3.c.a		1
28.d	even	2	1		176.3.h.a		1
35.c	odd	2	1		275.3.c.a		1
35.f	even	4	2		275.3.d.a		2
56.e	even	2	1		704.3.h.a		1
56.h	odd	2	1		704.3.h.b		1
77.b	even	2	1		11.3.b.a	✓	1
77.j	odd	10	4		121.3.d.b		4
77.l	even	10	4		121.3.d.b		4
84.h	odd	2	1		1584.3.j.a		1
231.h	odd	2	1		99.3.c.a		1
308.g	odd	2	1		176.3.h.a		1
385.h	even	2	1		275.3.c.a		1
385.l	odd	4	2		275.3.d.a		2
616.g	odd	2	1		704.3.h.a		1
616.o	even	2	1		704.3.h.b		1
924.n	even	2	1		1584.3.j.a		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
11.3.b.a	✓	1	7.b	odd	2	1
11.3.b.a	✓	1	77.b	even	2	1
99.3.c.a		1	21.c	even	2	1
99.3.c.a		1	231.h	odd	2	1
121.3.d.b		4	77.j	odd	10	4
121.3.d.b		4	77.l	even	10	4
176.3.h.a		1	28.d	even	2	1
176.3.h.a		1	308.g	odd	2	1
275.3.c.a		1	35.c	odd	2	1
275.3.c.a		1	385.h	even	2	1
275.3.d.a		2	35.f	even	4	2
275.3.d.a		2	385.l	odd	4	2
539.3.c.a		1	1.a	even	1	1	trivial
539.3.c.a		1	11.b	odd	2	1	CM
704.3.h.a		1	56.e	even	2	1
704.3.h.a		1	616.g	odd	2	1
704.3.h.b		1	56.h	odd	2	1
704.3.h.b		1	616.o	even	2	1
1584.3.j.a		1	84.h	odd	2	1
1584.3.j.a		1	924.n	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(539, [\chi])\):

\( T_{2} \)

\( T_{3} - 5 \)

Hecke characteristic polynomials

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