Newform orbit 572.2.m.a

• Label: 572.2.m.a
• Level: $572$
• Weight: $2$
• Character orbit: 572.m
• Analytic conductor: $4.567$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.56744299562\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 28 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
21.1		0		−2.66794				0		0.155603	+	0.155603i		0		−0.218446	−	0.218446i		0		4.11791				0
21.2		0		−2.66794				0		0.155603	+	0.155603i		0		0.218446	+	0.218446i		0		4.11791				0
21.3		0		−1.92499				0		−2.81451	−	2.81451i		0		−2.52515	−	2.52515i		0		0.705586				0
21.4		0		−1.92499				0		−2.81451	−	2.81451i		0		2.52515	+	2.52515i		0		0.705586				0
21.5		0		−1.70981				0		2.12487	+	2.12487i		0		−2.56856	−	2.56856i		0		−0.0765454				0
21.6		0		−1.70981				0		2.12487	+	2.12487i		0		2.56856	+	2.56856i		0		−0.0765454				0
21.7		0		0.316705				0		−1.15567	−	1.15567i		0		−0.758144	−	0.758144i		0		−2.89970				0
21.8		0		0.316705				0		−1.15567	−	1.15567i		0		0.758144	+	0.758144i		0		−2.89970				0
21.9		0		0.950141				0		−0.290933	−	0.290933i		0		−3.15373	−	3.15373i		0		−2.09723				0
21.10		0		0.950141				0		−0.290933	−	0.290933i		0		3.15373	+	3.15373i		0		−2.09723				0
21.11		0		1.98417				0		2.59618	+	2.59618i		0		−1.56213	−	1.56213i		0		0.936925				0
21.12		0		1.98417				0		2.59618	+	2.59618i		0		1.56213	+	1.56213i		0		0.936925				0
21.13		0		3.05173				0		−0.615537	−	0.615537i		0		−1.73706	−	1.73706i		0		6.31305				0
21.14		0		3.05173				0		−0.615537	−	0.615537i		0		1.73706	+	1.73706i		0		6.31305				0
109.1		0		−2.66794				0		0.155603	−	0.155603i		0		−0.218446	+	0.218446i		0		4.11791				0
109.2		0		−2.66794				0		0.155603	−	0.155603i		0		0.218446	−	0.218446i		0		4.11791				0
109.3		0		−1.92499				0		−2.81451	+	2.81451i		0		−2.52515	+	2.52515i		0		0.705586				0
109.4		0		−1.92499				0		−2.81451	+	2.81451i		0		2.52515	−	2.52515i		0		0.705586				0
109.5		0		−1.70981				0		2.12487	−	2.12487i		0		−2.56856	+	2.56856i		0		−0.0765454				0
109.6		0		−1.70981				0		2.12487	−	2.12487i		0		2.56856	−	2.56856i		0		−0.0765454				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.b	odd	2	1	inner
13.d	odd	4	1	inner
143.g	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	572.2.m.a	✓	28
11.b	odd	2	1	inner	572.2.m.a	✓	28
13.d	odd	4	1	inner	572.2.m.a	✓	28
143.g	even	4	1	inner	572.2.m.a	✓	28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
572.2.m.a	✓	28	1.a	even	1	1	trivial
572.2.m.a	✓	28	11.b	odd	2	1	inner
572.2.m.a	✓	28	13.d	odd	4	1	inner
572.2.m.a	✓	28	143.g	even	4	1	inner

Hecke kernels

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