Newform orbit 572.2.b.c

• Label: 572.2.b.c
• Level: $572$
• Weight: $2$
• Character orbit: 572.b
• Analytic conductor: $4.567$
• Analytic rank: $0$
• Dimension: $56$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.56744299562\)
Analytic rank:	\(0\)
Dimension:	\(56\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 56 q + 4 q^{4} - 32 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
571.1	−1.41153	−	0.0870114i			2.50968i	1.98486	+	0.245639i		−	2.92941i	0.218370	−	3.54249i			1.23786i	−2.78032	−	0.519434i	−3.29847			−0.254892	+	4.13496i
571.2	−1.41153	−	0.0870114i			2.50968i	1.98486	+	0.245639i			2.92941i	0.218370	−	3.54249i			1.23786i	−2.78032	−	0.519434i	−3.29847			0.254892	−	4.13496i
571.3	−1.41153	+	0.0870114i		−	2.50968i	1.98486	−	0.245639i		−	2.92941i	0.218370	+	3.54249i		−	1.23786i	−2.78032	+	0.519434i	−3.29847			0.254892	+	4.13496i
571.4	−1.41153	+	0.0870114i		−	2.50968i	1.98486	−	0.245639i			2.92941i	0.218370	+	3.54249i		−	1.23786i	−2.78032	+	0.519434i	−3.29847			−0.254892	−	4.13496i
571.5	−1.30250	−	0.550896i			0.566258i	1.39303	+	1.43509i		−	3.29519i	0.311949	−	0.737553i			2.02255i	−1.02384	−	2.63662i	2.67935			−1.81531	+	4.29199i
571.6	−1.30250	−	0.550896i			0.566258i	1.39303	+	1.43509i			3.29519i	0.311949	−	0.737553i			2.02255i	−1.02384	−	2.63662i	2.67935			1.81531	−	4.29199i
571.7	−1.30250	+	0.550896i		−	0.566258i	1.39303	−	1.43509i		−	3.29519i	0.311949	+	0.737553i		−	2.02255i	−1.02384	+	2.63662i	2.67935			1.81531	+	4.29199i
571.8	−1.30250	+	0.550896i		−	0.566258i	1.39303	−	1.43509i			3.29519i	0.311949	+	0.737553i		−	2.02255i	−1.02384	+	2.63662i	2.67935			−1.81531	−	4.29199i
571.9	−1.28473	−	0.591168i		−	1.41709i	1.30104	+	1.51898i		−	1.72500i	−0.837739	+	1.82057i		−	3.58187i	−0.773512	−	2.72060i	0.991852			−1.01976	+	2.21615i
571.10	−1.28473	−	0.591168i		−	1.41709i	1.30104	+	1.51898i			1.72500i	−0.837739	+	1.82057i		−	3.58187i	−0.773512	−	2.72060i	0.991852			1.01976	−	2.21615i
571.11	−1.28473	+	0.591168i			1.41709i	1.30104	−	1.51898i		−	1.72500i	−0.837739	−	1.82057i			3.58187i	−0.773512	+	2.72060i	0.991852			1.01976	+	2.21615i
571.12	−1.28473	+	0.591168i			1.41709i	1.30104	−	1.51898i			1.72500i	−0.837739	−	1.82057i			3.58187i	−0.773512	+	2.72060i	0.991852			−1.01976	−	2.21615i
571.13	−0.913620	−	1.07949i			1.67751i	−0.330598	+	1.97249i		−	1.10479i	1.81085	−	1.53260i		−	1.27047i	2.43132	−	1.44523i	0.185967			−1.19260	+	1.00935i
571.14	−0.913620	−	1.07949i			1.67751i	−0.330598	+	1.97249i			1.10479i	1.81085	−	1.53260i		−	1.27047i	2.43132	−	1.44523i	0.185967			1.19260	−	1.00935i
571.15	−0.913620	+	1.07949i		−	1.67751i	−0.330598	−	1.97249i		−	1.10479i	1.81085	+	1.53260i			1.27047i	2.43132	+	1.44523i	0.185967			1.19260	+	1.00935i
571.16	−0.913620	+	1.07949i		−	1.67751i	−0.330598	−	1.97249i			1.10479i	1.81085	+	1.53260i			1.27047i	2.43132	+	1.44523i	0.185967			−1.19260	−	1.00935i
571.17	−0.883550	−	1.10424i		−	2.47596i	−0.438678	+	1.95130i		−	2.76928i	−2.73405	+	2.18764i			0.534510i	2.54229	−	1.23966i	−3.13038			−3.05794	+	2.44680i
571.18	−0.883550	−	1.10424i		−	2.47596i	−0.438678	+	1.95130i			2.76928i	−2.73405	+	2.18764i			0.534510i	2.54229	−	1.23966i	−3.13038			3.05794	−	2.44680i
571.19	−0.883550	+	1.10424i			2.47596i	−0.438678	−	1.95130i		−	2.76928i	−2.73405	−	2.18764i		−	0.534510i	2.54229	+	1.23966i	−3.13038			3.05794	+	2.44680i
571.20	−0.883550	+	1.10424i			2.47596i	−0.438678	−	1.95130i			2.76928i	−2.73405	−	2.18764i		−	0.534510i	2.54229	+	1.23966i	−3.13038			−3.05794	−	2.44680i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
11.b	odd	2	1	inner
13.b	even	2	1	inner
44.c	even	2	1	inner
52.b	odd	2	1	inner
143.d	odd	2	1	inner
572.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	572.2.b.c	✓	56
4.b	odd	2	1	inner	572.2.b.c	✓	56
11.b	odd	2	1	inner	572.2.b.c	✓	56
13.b	even	2	1	inner	572.2.b.c	✓	56
44.c	even	2	1	inner	572.2.b.c	✓	56
52.b	odd	2	1	inner	572.2.b.c	✓	56
143.d	odd	2	1	inner	572.2.b.c	✓	56
572.b	even	2	1	inner	572.2.b.c	✓	56

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
572.2.b.c	✓	56	1.a	even	1	1	trivial
572.2.b.c	✓	56	4.b	odd	2	1	inner
572.2.b.c	✓	56	11.b	odd	2	1	inner
572.2.b.c	✓	56	13.b	even	2	1	inner
572.2.b.c	✓	56	44.c	even	2	1	inner
572.2.b.c	✓	56	52.b	odd	2	1	inner
572.2.b.c	✓	56	143.d	odd	2	1	inner
572.2.b.c	✓	56	572.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{14} + 25T_{3}^{12} + 241T_{3}^{10} + 1118T_{3}^{8} + 2535T_{3}^{6} + 2517T_{3}^{4} + 743T_{3}^{2} + 52 \) acting on \(S_{2}^{\mathrm{new}}(572, [\chi])\).