Newform orbit 531.5.c.c

• Label: 531.5.c.c
• Level: $531$
• Weight: $5$
• Character orbit: 531.c
• Analytic conductor: $54.889$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	531.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(54.8894503975\)
Analytic rank:	\(0\)
Dimension:	\(40\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 320 q^{4} + 80 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
235.1		−	1.60448i		0		13.4256			−43.0607				0		4.54722				−	47.2128i		0				69.0900i
235.2			1.60448i		0		13.4256			−43.0607				0		4.54722					47.2128i		0			−	69.0900i
235.3		−	5.29883i		0		−12.0776			42.4307				0		90.9935				−	20.7841i		0			−	224.833i
235.4			5.29883i		0		−12.0776			42.4307				0		90.9935					20.7841i		0				224.833i
235.5		−	6.38393i		0		−24.7546			−31.9236				0		−80.9493					55.8887i		0				203.798i
235.6			6.38393i		0		−24.7546			−31.9236				0		−80.9493				−	55.8887i		0			−	203.798i
235.7		−	7.53520i		0		−40.7793			27.3808				0		−9.32220					186.717i		0			−	206.320i
235.8			7.53520i		0		−40.7793			27.3808				0		−9.32220				−	186.717i		0				206.320i
235.9		−	5.19541i		0		−10.9923			−25.7756				0		−29.3633				−	26.0170i		0				133.915i
235.10			5.19541i		0		−10.9923			−25.7756				0		−29.3633					26.0170i		0			−	133.915i
235.11		−	3.19247i		0		5.80813			−19.3766				0		−18.8230				−	69.6218i		0				61.8591i
235.12			3.19247i		0		5.80813			−19.3766				0		−18.8230					69.6218i		0			−	61.8591i
235.13		−	1.57441i		0		13.5212			−17.7411				0		−72.1808				−	46.4785i		0				27.9317i
235.14			1.57441i		0		13.5212			−17.7411				0		−72.1808					46.4785i		0			−	27.9317i
235.15		−	4.61769i		0		−5.32309			−11.3540				0		27.8583				−	49.3027i		0				52.4293i
235.16			4.61769i		0		−5.32309			−11.3540				0		27.8583					49.3027i		0			−	52.4293i
235.17		−	7.01249i		0		−33.1751			−2.76773				0		46.3747					120.440i		0				19.4087i
235.18			7.01249i		0		−33.1751			−2.76773				0		46.3747				−	120.440i		0			−	19.4087i
235.19		−	1.28572i		0		14.3469			7.96483				0		60.8648				−	39.0175i		0			−	10.2405i
235.20			1.28572i		0		14.3469			7.96483				0		60.8648					39.0175i		0				10.2405i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
59.b	odd	2	1	inner
177.d	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	531.5.c.c	✓	40
3.b	odd	2	1	inner	531.5.c.c	✓	40
59.b	odd	2	1	inner	531.5.c.c	✓	40
177.d	even	2	1	inner	531.5.c.c	✓	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
531.5.c.c	✓	40	1.a	even	1	1	trivial
531.5.c.c	✓	40	3.b	odd	2	1	inner
531.5.c.c	✓	40	59.b	odd	2	1	inner
531.5.c.c	✓	40	177.d	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^20 + 240*T2^18 + 24103*T2^16 + 1317469*T2^14 + 42684634*T2^12 + 836622203*T2^10 + 9712327822*T2^8 + 62976337992*T2^6 + 209251902096*T2^4 + 331538861808*T2^2 + 197700577632