Newform orbit 572.2.bc.a

• Label: 572.2.bc.a
• Level: $572$
• Weight: $2$
• Character orbit: 572.bc
• Analytic conductor: $4.567$
• Analytic rank: $0$
• Dimension: $56$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bc (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.56744299562\)
Analytic rank:	\(0\)
Dimension:	\(56\)
Relative dimension:	\(14\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 56 q - 28 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
197.1		0		−1.56324	−	2.70762i		0		0.477789	−	0.477789i		0		−1.02740	−	3.83429i		0		−3.38745	+	5.86724i		0
197.2		0		−1.56324	−	2.70762i		0		0.477789	−	0.477789i		0		1.02740	+	3.83429i		0		−3.38745	+	5.86724i		0
197.3		0		−1.02435	−	1.77422i		0		−1.58636	+	1.58636i		0		−0.799284	−	2.98297i		0		−0.598575	+	1.03676i		0
197.4		0		−1.02435	−	1.77422i		0		−1.58636	+	1.58636i		0		0.799284	+	2.98297i		0		−0.598575	+	1.03676i		0
197.5		0		−0.425370	−	0.736762i		0		2.35532	−	2.35532i		0		−0.337440	−	1.25934i		0		1.13812	−	1.97128i		0
197.6		0		−0.425370	−	0.736762i		0		2.35532	−	2.35532i		0		0.337440	+	1.25934i		0		1.13812	−	1.97128i		0
197.7		0		−0.308749	−	0.534769i		0		−1.59856	+	1.59856i		0		−0.412876	−	1.54087i		0		1.30935	−	2.26786i		0
197.8		0		−0.308749	−	0.534769i		0		−1.59856	+	1.59856i		0		0.412876	+	1.54087i		0		1.30935	−	2.26786i		0
197.9		0		0.591694	+	1.02484i		0		0.335170	−	0.335170i		0		−0.719487	−	2.68516i		0		0.799795	−	1.38529i		0
197.10		0		0.591694	+	1.02484i		0		0.335170	−	0.335170i		0		0.719487	+	2.68516i		0		0.799795	−	1.38529i		0
197.11		0		1.26462	+	2.19039i		0		−2.02978	+	2.02978i		0		−0.531478	−	1.98350i		0		−1.69853	+	2.94193i		0
197.12		0		1.26462	+	2.19039i		0		−2.02978	+	2.02978i		0		0.531478	+	1.98350i		0		−1.69853	+	2.94193i		0
197.13		0		1.46539	+	2.53814i		0		2.04642	−	2.04642i		0		−1.22814	−	4.58348i		0		−2.79476	+	4.84067i		0
197.14		0		1.46539	+	2.53814i		0		2.04642	−	2.04642i		0		1.22814	+	4.58348i		0		−2.79476	+	4.84067i		0
241.1		0		−1.56324	+	2.70762i		0		0.477789	+	0.477789i		0		−1.02740	+	3.83429i		0		−3.38745	−	5.86724i		0
241.2		0		−1.56324	+	2.70762i		0		0.477789	+	0.477789i		0		1.02740	−	3.83429i		0		−3.38745	−	5.86724i		0
241.3		0		−1.02435	+	1.77422i		0		−1.58636	−	1.58636i		0		−0.799284	+	2.98297i		0		−0.598575	−	1.03676i		0
241.4		0		−1.02435	+	1.77422i		0		−1.58636	−	1.58636i		0		0.799284	−	2.98297i		0		−0.598575	−	1.03676i		0
241.5		0		−0.425370	+	0.736762i		0		2.35532	+	2.35532i		0		−0.337440	+	1.25934i		0		1.13812	+	1.97128i		0
241.6		0		−0.425370	+	0.736762i		0		2.35532	+	2.35532i		0		0.337440	−	1.25934i		0		1.13812	+	1.97128i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.b	odd	2	1	inner
13.f	odd	12	1	inner
143.o	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	572.2.bc.a	✓	56
11.b	odd	2	1	inner	572.2.bc.a	✓	56
13.f	odd	12	1	inner	572.2.bc.a	✓	56
143.o	even	12	1	inner	572.2.bc.a	✓	56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
572.2.bc.a	✓	56	1.a	even	1	1	trivial
572.2.bc.a	✓	56	11.b	odd	2	1	inner
572.2.bc.a	✓	56	13.f	odd	12	1	inner
572.2.bc.a	✓	56	143.o	even	12	1	inner

Hecke kernels

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