Newform orbit 572.2.p.a

• Label: 572.2.p.a
• Level: $572$
• Weight: $2$
• Character orbit: 572.p
• Analytic conductor: $4.567$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.56744299562\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
309.1		0		−1.63981	−	2.84024i		0				0.829371i		0		0.846479	+	0.488715i		0		−3.87798	+	6.71686i		0
309.2		0		−1.16394	−	2.01600i		0			−	3.47989i		0		−0.907365	−	0.523867i		0		−1.20951	+	2.09493i		0
309.3		0		−1.07694	−	1.86531i		0				3.60411i		0		−3.54414	−	2.04621i		0		−0.819590	+	1.41957i		0
309.4		0		−0.909010	−	1.57445i		0				1.10453i		0		0.391551	+	0.226062i		0		−0.152598	+	0.264307i		0
309.5		0		−0.780208	−	1.35136i		0			−	0.661534i		0		3.95034	+	2.28073i		0		0.282552	−	0.489394i		0
309.6		0		−0.308986	−	0.535180i		0			−	3.59217i		0		−1.27174	−	0.734239i		0		1.30905	−	2.26735i		0
309.7		0		0.0659947	+	0.114306i		0				0.505374i		0		−3.35869	−	1.93914i		0		1.49129	−	2.58299i		0
309.8		0		0.196667	+	0.340638i		0				4.15244i		0		2.01581	+	1.16383i		0		1.42264	−	2.46409i		0
309.9		0		0.716368	+	1.24079i		0			−	2.80197i		0		4.48758	+	2.59090i		0		0.473633	−	0.820357i		0
309.10		0		0.994483	+	1.72249i		0			−	2.64929i		0		−0.165013	−	0.0952705i		0		−0.477992	+	0.827907i		0
309.11		0		1.44478	+	2.50242i		0				0.307799i		0		−1.50558	−	0.869246i		0		−2.67475	+	4.63280i		0
309.12		0		1.46061	+	2.52985i		0				2.68122i		0		2.06077	+	1.18978i		0		−2.76675	+	4.79215i		0
485.1		0		−1.63981	+	2.84024i		0			−	0.829371i		0		0.846479	−	0.488715i		0		−3.87798	−	6.71686i		0
485.2		0		−1.16394	+	2.01600i		0				3.47989i		0		−0.907365	+	0.523867i		0		−1.20951	−	2.09493i		0
485.3		0		−1.07694	+	1.86531i		0			−	3.60411i		0		−3.54414	+	2.04621i		0		−0.819590	−	1.41957i		0
485.4		0		−0.909010	+	1.57445i		0			−	1.10453i		0		0.391551	−	0.226062i		0		−0.152598	−	0.264307i		0
485.5		0		−0.780208	+	1.35136i		0				0.661534i		0		3.95034	−	2.28073i		0		0.282552	+	0.489394i		0
485.6		0		−0.308986	+	0.535180i		0				3.59217i		0		−1.27174	+	0.734239i		0		1.30905	+	2.26735i		0
485.7		0		0.0659947	−	0.114306i		0			−	0.505374i		0		−3.35869	+	1.93914i		0		1.49129	+	2.58299i		0
485.8		0		0.196667	−	0.340638i		0			−	4.15244i		0		2.01581	−	1.16383i		0		1.42264	+	2.46409i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
13.e	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	572.2.p.a	✓	24
13.e	even	6	1	inner	572.2.p.a	✓	24
13.f	odd	12	1		7436.2.a.u		12
13.f	odd	12	1		7436.2.a.v		12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
572.2.p.a	✓	24	1.a	even	1	1	trivial
572.2.p.a	✓	24	13.e	even	6	1	inner
7436.2.a.u		12	13.f	odd	12	1
7436.2.a.v		12	13.f	odd	12	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(572, [\chi])\).