Newform orbit 2520.2.em.b

• Label: 2520.2.em.b
• Level: $2520$
• Weight: $2$
• Character orbit: 2520.em
• Analytic conductor: $20.122$
• Analytic rank: $0$
• Dimension: $32$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2520.em (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(20.1223013094\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 32 * q + 16 * q^5 + 4 * q^7 - 12 * q^19 - 12 * q^23 - 16 * q^25 - 12 * q^31 - 4 * q^35 - 12 * q^37 - 16 * q^41 - 8 * q^43 - 8 * q^47 - 20 * q^49 - 24 * q^59 + 12 * q^65 + 12 * q^67 + 12 * q^73 - 8 * q^77 + 4 * q^79 + 32 * q^83 + 24 * q^89 + 16 * q^91 - 12 * q^95

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
521.1		0			0			0		0.500000	+	0.866025i		0		−2.64501	+	0.0624190i		0			0			0
521.2		0			0			0		0.500000	+	0.866025i		0		−2.20274	+	1.46558i		0			0			0
521.3		0			0			0		0.500000	+	0.866025i		0		−1.82582	−	1.91478i		0			0			0
521.4		0			0			0		0.500000	+	0.866025i		0		−1.48143	−	2.19212i		0			0			0
521.5		0			0			0		0.500000	+	0.866025i		0		−1.39155	+	2.25024i		0			0			0
521.6		0			0			0		0.500000	+	0.866025i		0		−1.26820	+	2.32199i		0			0			0
521.7		0			0			0		0.500000	+	0.866025i		0		−0.968349	−	2.46217i		0			0			0
521.8		0			0			0		0.500000	+	0.866025i		0		−0.549659	+	2.58803i		0			0			0
521.9		0			0			0		0.500000	+	0.866025i		0		0.907873	+	2.48511i		0			0			0
521.10		0			0			0		0.500000	+	0.866025i		0		1.05190	−	2.42765i		0			0			0
521.11		0			0			0		0.500000	+	0.866025i		0		1.24223	−	2.33599i		0			0			0
521.12		0			0			0		0.500000	+	0.866025i		0		1.70845	+	2.02020i		0			0			0
521.13		0			0			0		0.500000	+	0.866025i		0		1.96264	+	1.77427i		0			0			0
521.14		0			0			0		0.500000	+	0.866025i		0		2.34176	−	1.23133i		0			0			0
521.15		0			0			0		0.500000	+	0.866025i		0		2.47514	+	0.934711i		0			0			0
521.16		0			0			0		0.500000	+	0.866025i		0		2.64277	+	0.125595i		0			0			0
1601.1		0			0			0		0.500000	−	0.866025i		0		−2.64501	−	0.0624190i		0			0			0
1601.2		0			0			0		0.500000	−	0.866025i		0		−2.20274	−	1.46558i		0			0			0
1601.3		0			0			0		0.500000	−	0.866025i		0		−1.82582	+	1.91478i		0			0			0
1601.4		0			0			0		0.500000	−	0.866025i		0		−1.48143	+	2.19212i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
21.g	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2520.2.em.b	yes	32
3.b	odd	2	1		2520.2.em.a	✓	32
7.d	odd	6	1		2520.2.em.a	✓	32
21.g	even	6	1	inner	2520.2.em.b	yes	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2520.2.em.a	✓	32	3.b	odd	2	1
2520.2.em.a	✓	32	7.d	odd	6	1
2520.2.em.b	yes	32	1.a	even	1	1	trivial
2520.2.em.b	yes	32	21.g	even	6	1	inner