Newform orbit 536.5.b.a

• Label: 536.5.b.a
• Level: $536$
• Weight: $5$
• Character orbit: 536.b
• Analytic conductor: $55.406$
• Analytic rank: $0$
• Dimension: $68$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 536 = 2^{3} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	536.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(55.4063002129\)
Analytic rank:	\(0\)
Dimension:	\(68\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 68 q - 1636 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
401.1		0			−	17.4672i		0			−	18.8633i		0			−	31.5978i		0		−224.104				0
401.2		0			−	17.2467i		0			−	7.44497i		0			−	7.06749i		0		−216.449				0
401.3		0			−	16.4204i		0				32.3147i		0			−	24.9595i		0		−188.629				0
401.4		0			−	15.4275i		0				2.31434i		0				97.6680i		0		−157.008				0
401.5		0			−	14.2504i		0				37.1510i		0				36.8298i		0		−122.075				0
401.6		0			−	14.1329i		0			−	39.4195i		0			−	22.1399i		0		−118.740				0
401.7		0			−	14.0401i		0				34.1237i		0			−	85.5448i		0		−116.124				0
401.8		0			−	13.9413i		0			−	24.3271i		0				64.6265i		0		−113.360				0
401.9		0			−	13.5583i		0				19.6755i		0				42.9512i		0		−102.827				0
401.10		0			−	13.5251i		0				26.3678i		0				12.8147i		0		−101.928				0
401.11		0			−	12.3314i		0				25.0104i		0			−	88.4567i		0		−71.0635				0
401.12		0			−	11.7770i		0				6.09314i		0			−	34.9607i		0		−57.6985				0
401.13		0			−	11.5996i		0			−	14.4941i		0				19.5453i		0		−53.5512				0
401.14		0			−	10.6710i		0			−	41.1984i		0			−	54.1432i		0		−32.8693				0
401.15		0			−	9.40453i		0			−	46.7850i		0			−	56.1382i		0		−7.44522				0
401.16		0			−	9.35399i		0				44.6342i		0				91.9402i		0		−6.49717				0
401.17		0			−	9.19454i		0			−	9.04779i		0			−	34.6002i		0		−3.53964				0
401.18		0			−	9.10854i		0			−	23.8430i		0				51.3411i		0		−1.96551				0
401.19		0			−	8.95505i		0			−	33.0647i		0				54.1992i		0		0.807160				0
401.20		0			−	8.79182i		0			−	4.41061i		0			−	59.4255i		0		3.70390				0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	536.5.b.a	✓	68
67.b	odd	2	1	inner	536.5.b.a	✓	68

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
536.5.b.a	✓	68	1.a	even	1	1	trivial
536.5.b.a	✓	68	67.b	odd	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(536, [\chi])\).