Newform orbit 531.4.d.a

• Label: 531.4.d.a
• Level: $531$
• Weight: $4$
• Character orbit: 531.d
• Analytic conductor: $31.330$
• Analytic rank: $0$
• Dimension: $60$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	531.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(31.3300142130\)
Analytic rank:	\(0\)
Dimension:	\(60\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 60 q + 240 q^{4} + 24 q^{7} + 816 q^{16} - 96 q^{22} - 2004 q^{25} - 576 q^{28} + 1248 q^{46} + 5172 q^{49} + 816 q^{64} + 2784 q^{76} + 1992 q^{79} + 2688 q^{85} - 9576 q^{88} + 672 q^{94}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
530.1	−5.38598				0		21.0088				−	8.70296i		0		19.2691			−70.0651				0				46.8740i
530.2	−5.38598				0		21.0088					8.70296i		0		19.2691			−70.0651				0			−	46.8740i
530.3	−5.10709				0		18.0823				−	11.0008i		0		−35.1570			−51.4913				0				56.1819i
530.4	−5.10709				0		18.0823					11.0008i		0		−35.1570			−51.4913				0			−	56.1819i
530.5	−4.87972				0		15.8116				−	2.08030i		0		−9.27371			−38.1185				0				10.1513i
530.6	−4.87972				0		15.8116					2.08030i		0		−9.27371			−38.1185				0			−	10.1513i
530.7	−4.82853				0		15.3147				−	20.4999i		0		27.0026			−35.3195				0				98.9847i
530.8	−4.82853				0		15.3147					20.4999i		0		27.0026			−35.3195				0			−	98.9847i
530.9	−4.19390				0		9.58884				−	9.04091i		0		−1.21513			−6.66343				0				37.9167i
530.10	−4.19390				0		9.58884					9.04091i		0		−1.21513			−6.66343				0			−	37.9167i
530.11	−3.94706				0		7.57932					21.2511i		0		−20.5183			1.66045				0			−	83.8794i
530.12	−3.94706				0		7.57932				−	21.2511i		0		−20.5183			1.66045				0				83.8794i
530.13	−3.35507				0		3.25649					5.32423i		0		4.49346			15.9148				0			−	17.8632i
530.14	−3.35507				0		3.25649				−	5.32423i		0		4.49346			15.9148				0				17.8632i
530.15	−3.26742				0		2.67606					14.5237i		0		−9.44552			17.3956				0			−	47.4550i
530.16	−3.26742				0		2.67606				−	14.5237i		0		−9.44552			17.3956				0				47.4550i
530.17	−3.16009				0		1.98619				−	1.99616i		0		22.5873			19.0042				0				6.30804i
530.18	−3.16009				0		1.98619					1.99616i		0		22.5873			19.0042				0			−	6.30804i
530.19	−2.05755				0		−3.76647					20.7416i		0		26.5362			24.2101				0			−	42.6769i
530.20	−2.05755				0		−3.76647				−	20.7416i		0		26.5362			24.2101				0				42.6769i

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	531.4.d.a	✓	60
3.b	odd	2	1	inner	531.4.d.a	✓	60
59.b	odd	2	1	inner	531.4.d.a	✓	60
177.d	even	2	1	inner	531.4.d.a	✓	60

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
531.4.d.a	✓	60	1.a	even	1	1	trivial
531.4.d.a	✓	60	3.b	odd	2	1	inner
531.4.d.a	✓	60	59.b	odd	2	1	inner
531.4.d.a	✓	60	177.d	even	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(531, [\chi])\).