Newform orbit 5520.2.be.d

• Label: 5520.2.be.d
• Level: $5520$
• Weight: $2$
• Character orbit: 5520.be
• Analytic conductor: $44.077$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5520.be (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(44.0774219157\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1471.1		0			−	1.00000i		0				1.00000i		0		−3.34851				0		−1.00000				0
1471.2		0				1.00000i		0			−	1.00000i		0		−3.34851				0		−1.00000				0
1471.3		0			−	1.00000i		0				1.00000i		0		1.52302				0		−1.00000				0
1471.4		0				1.00000i		0			−	1.00000i		0		1.52302				0		−1.00000				0
1471.5		0			−	1.00000i		0				1.00000i		0		−3.12483				0		−1.00000				0
1471.6		0				1.00000i		0			−	1.00000i		0		−3.12483				0		−1.00000				0
1471.7		0			−	1.00000i		0				1.00000i		0		−3.67125				0		−1.00000				0
1471.8		0				1.00000i		0			−	1.00000i		0		−3.67125				0		−1.00000				0
1471.9		0			−	1.00000i		0				1.00000i		0		1.53388				0		−1.00000				0
1471.10		0				1.00000i		0			−	1.00000i		0		1.53388				0		−1.00000				0
1471.11		0			−	1.00000i		0				1.00000i		0		2.13359				0		−1.00000				0
1471.12		0				1.00000i		0			−	1.00000i		0		2.13359				0		−1.00000				0
1471.13		0			−	1.00000i		0				1.00000i		0		3.74981				0		−1.00000				0
1471.14		0				1.00000i		0			−	1.00000i		0		3.74981				0		−1.00000				0
1471.15		0			−	1.00000i		0				1.00000i		0		−3.60511				0		−1.00000				0
1471.16		0				1.00000i		0			−	1.00000i		0		−3.60511				0		−1.00000				0
1471.17		0			−	1.00000i		0				1.00000i		0		0.143131				0		−1.00000				0
1471.18		0				1.00000i		0			−	1.00000i		0		0.143131				0		−1.00000				0
1471.19		0			−	1.00000i		0				1.00000i		0		2.01693				0		−1.00000				0
1471.20		0				1.00000i		0			−	1.00000i		0		2.01693				0		−1.00000				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
92.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	5520.2.be.d	yes	32
4.b	odd	2	1		5520.2.be.c	✓	32
23.b	odd	2	1		5520.2.be.c	✓	32
92.b	even	2	1	inner	5520.2.be.d	yes	32

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
5520.2.be.c	✓	32	4.b	odd	2	1
5520.2.be.c	✓	32	23.b	odd	2	1
5520.2.be.d	yes	32	1.a	even	1	1	trivial
5520.2.be.d	yes	32	92.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T7^16 - 4*T7^15 - 61*T7^14 + 220*T7^13 + 1519*T7^12 - 4876*T7^11 - 19571*T7^10 + 56420*T7^9 + 137556*T7^8 - 367664*T7^7 - 515276*T7^6 + 1335632*T7^5 + 915168*T7^4 - 2472448*T7^3 - 485120*T7^2 + 1790976*T7 - 239616