Newform orbit 4620.2.be.e

• Label: 4620.2.be.e
• Level: $4620$
• Weight: $2$
• Character orbit: 4620.be
• Analytic conductor: $36.891$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 4620 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4620.be (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(36.8908857338\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 32 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3541.1		0			−	1.00000i		0				1.00000i		0		−2.41862	+	1.07251i		0		−1.00000				0
3541.2		0				1.00000i		0			−	1.00000i		0		−2.41862	−	1.07251i		0		−1.00000				0
3541.3		0			−	1.00000i		0				1.00000i		0		−1.00169	+	2.44880i		0		−1.00000				0
3541.4		0				1.00000i		0			−	1.00000i		0		−1.00169	−	2.44880i		0		−1.00000				0
3541.5		0			−	1.00000i		0				1.00000i		0		−1.62630	−	2.08690i		0		−1.00000				0
3541.6		0				1.00000i		0			−	1.00000i		0		−1.62630	+	2.08690i		0		−1.00000				0
3541.7		0			−	1.00000i		0				1.00000i		0		−1.30875	+	2.29939i		0		−1.00000				0
3541.8		0				1.00000i		0			−	1.00000i		0		−1.30875	−	2.29939i		0		−1.00000				0
3541.9		0			−	1.00000i		0				1.00000i		0		1.00169	−	2.44880i		0		−1.00000				0
3541.10		0				1.00000i		0			−	1.00000i		0		1.00169	+	2.44880i		0		−1.00000				0
3541.11		0			−	1.00000i		0				1.00000i		0		1.94098	+	1.79794i		0		−1.00000				0
3541.12		0				1.00000i		0			−	1.00000i		0		1.94098	−	1.79794i		0		−1.00000				0
3541.13		0			−	1.00000i		0				1.00000i		0		−1.69334	−	2.03288i		0		−1.00000				0
3541.14		0				1.00000i		0			−	1.00000i		0		−1.69334	+	2.03288i		0		−1.00000				0
3541.15		0			−	1.00000i		0				1.00000i		0		2.64445	−	0.0830154i		0		−1.00000				0
3541.16		0				1.00000i		0			−	1.00000i		0		2.64445	+	0.0830154i		0		−1.00000				0
3541.17		0			−	1.00000i		0				1.00000i		0		−1.94098	−	1.79794i		0		−1.00000				0
3541.18		0				1.00000i		0			−	1.00000i		0		−1.94098	+	1.79794i		0		−1.00000				0
3541.19		0			−	1.00000i		0				1.00000i		0		2.41862	−	1.07251i		0		−1.00000				0
3541.20		0				1.00000i		0			−	1.00000i		0		2.41862	+	1.07251i		0		−1.00000				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	inner
11.b	odd	2	1	inner
77.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	4620.2.be.e	✓	32
7.b	odd	2	1	inner	4620.2.be.e	✓	32
11.b	odd	2	1	inner	4620.2.be.e	✓	32
77.b	even	2	1	inner	4620.2.be.e	✓	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
4620.2.be.e	✓	32	1.a	even	1	1	trivial
4620.2.be.e	✓	32	7.b	odd	2	1	inner
4620.2.be.e	✓	32	11.b	odd	2	1	inner
4620.2.be.e	✓	32	77.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T13^16 - 116*T13^14 + 4836*T13^12 - 92240*T13^10 + 913408*T13^8 - 4876992*T13^6 + 13486336*T13^4 - 16260096*T13^2 + 4194304