Newform orbit 528.6.o.b

• Label: 528.6.o.b
• Level: $528$
• Weight: $6$
• Character orbit: 528.o
• Analytic conductor: $84.683$
• Analytic rank: $0$
• Dimension: $40$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	528.o (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(84.6826568613\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q + 88 q^{5} - 3240 q^{9} + 5464 q^{25} + 6840 q^{33} + 4576 q^{37} - 7128 q^{45} + 58760 q^{49} - 165336 q^{53} + 16632 q^{69} + 28136 q^{77} + 262440 q^{81} - 304608 q^{89} + 102672 q^{93} + 15664 q^{97}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
175.1		0			−	9.00000i		0		−34.2910				0		120.607				0		−81.0000				0
175.2		0				9.00000i		0		−34.2910				0		120.607				0		−81.0000				0
175.3		0			−	9.00000i		0		89.8188				0		112.074				0		−81.0000				0
175.4		0				9.00000i		0		89.8188				0		112.074				0		−81.0000				0
175.5		0			−	9.00000i		0		89.8188				0		−112.074				0		−81.0000				0
175.6		0				9.00000i		0		89.8188				0		−112.074				0		−81.0000				0
175.7		0			−	9.00000i		0		48.1562				0		32.4843				0		−81.0000				0
175.8		0				9.00000i		0		48.1562				0		32.4843				0		−81.0000				0
175.9		0			−	9.00000i		0		−76.1886				0		−138.380				0		−81.0000				0
175.10		0				9.00000i		0		−76.1886				0		−138.380				0		−81.0000				0
175.11		0			−	9.00000i		0		57.6896				0		131.273				0		−81.0000				0
175.12		0				9.00000i		0		57.6896				0		131.273				0		−81.0000				0
175.13		0			−	9.00000i		0		4.87261				0		−228.204				0		−81.0000				0
175.14		0				9.00000i		0		4.87261				0		−228.204				0		−81.0000				0
175.15		0			−	9.00000i		0		1.95371				0		−158.286				0		−81.0000				0
175.16		0				9.00000i		0		1.95371				0		−158.286				0		−81.0000				0
175.17		0			−	9.00000i		0		−84.4799				0		98.5983				0		−81.0000				0
175.18		0				9.00000i		0		−84.4799				0		98.5983				0		−81.0000				0
175.19		0			−	9.00000i		0		1.95371				0		158.286				0		−81.0000				0
175.20		0				9.00000i		0		1.95371				0		158.286				0		−81.0000				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
11.b	odd	2	1	inner
44.c	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	528.6.o.b	✓	40
4.b	odd	2	1	inner	528.6.o.b	✓	40
11.b	odd	2	1	inner	528.6.o.b	✓	40
44.c	even	2	1	inner	528.6.o.b	✓	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
528.6.o.b	✓	40	1.a	even	1	1	trivial
528.6.o.b	✓	40	4.b	odd	2	1	inner
528.6.o.b	✓	40	11.b	odd	2	1	inner
528.6.o.b	✓	40	44.c	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^10 - 22*T5^9 - 16066*T5^8 + 342128*T5^7 + 84406964*T5^6 - 1715540152*T5^5 - 167515486856*T5^4 + 2600273179008*T5^3 + 113916977752704*T5^2 - 841327880579712*T5 + 1191984390880128