Newform orbit 572.2.s.a

• Label: 572.2.s.a
• Level: $572$
• Weight: $2$
• Character orbit: 572.s
• Analytic conductor: $4.567$
• Analytic rank: $0$
• Dimension: $160$
• CM: no
• Inner twists: $8$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(4.56744299562\)
Analytic rank:	\(0\)
Dimension:	\(160\)
Relative dimension:	\(80\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 160 q - 2 q^{4} + 68 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
43.1	−1.41333	+	0.0501117i	1.83041	+	1.05679i	1.99498	−	0.141648i		−	1.43229i	−2.63992	−	1.40186i	1.20221	−	0.694098i	−2.81245	+	0.300167i	0.733590	+	1.27062i	0.0717746	+	2.02430i
43.2	−1.41298	+	0.0591092i	−2.54803	−	1.47111i	1.99301	−	0.167040i		−	3.95496i	3.68727	+	1.92803i	−2.41626	+	1.39503i	−2.80621	+	0.353829i	2.82830	+	4.89877i	0.233775	+	5.58827i
43.3	−1.40920	−	0.118969i	−2.07307	−	1.19689i	1.97169	+	0.335302i			0.562219i	2.77898	+	1.93329i	−0.112468	+	0.0649336i	−2.73862	−	0.707079i	1.36509	+	2.36441i	0.0668866	−	0.792279i
43.4	−1.40794	−	0.133100i	1.15080	+	0.664413i	1.96457	+	0.374794i			4.34420i	−1.53182	−	1.08862i	−0.561519	+	0.324193i	−2.71610	−	0.789171i	−0.617110	−	1.06887i	0.578214	−	6.11635i
43.5	−1.40175	+	0.187369i	0.461021	+	0.266170i	1.92979	−	0.525287i		−	0.718470i	−0.696106	−	0.286722i	−3.26467	+	1.88486i	−2.60665	+	1.09790i	−1.35831	−	2.35266i	0.134619	+	1.00711i
43.6	−1.37518	+	0.329974i	−0.622539	−	0.359423i	1.78223	−	0.907548i		−	2.91525i	0.974703	+	0.288849i	4.00752	−	2.31374i	−2.15142	+	1.83613i	−1.24163	−	2.15057i	0.961958	+	4.00899i
43.7	−1.36236	+	0.379439i	−2.49055	−	1.43792i	1.71205	−	1.03387i			3.07981i	3.93863	+	1.01395i	1.00977	−	0.582994i	−1.94014	+	2.05812i	2.63522	+	4.56434i	−1.16860	−	4.19581i
43.8	−1.35805	−	0.394577i	−1.01294	−	0.584824i	1.68862	+	1.07171i			1.81934i	1.14487	+	1.19391i	−2.82002	+	1.62814i	−1.87036	−	2.12173i	−0.815963	−	1.41329i	0.717869	−	2.47076i
43.9	−1.32499	+	0.494359i	−0.498527	−	0.287825i	1.51122	−	1.31004i			1.29030i	0.802835	+	0.134915i	0.822321	−	0.474767i	−1.35473	+	2.48289i	−1.33431	−	2.31110i	−0.637872	−	1.70964i
43.10	−1.31800	−	0.512708i	2.39320	+	1.38172i	1.47426	+	1.35150i		−	1.60862i	−2.44583	−	3.04812i	0.824322	−	0.475923i	−1.25015	−	2.53715i	2.31828	+	4.01537i	−0.824753	+	2.12017i
43.11	−1.30032	−	0.556038i	0.593637	+	0.342737i	1.38164	+	1.44605i		−	3.22106i	−0.581342	−	0.775751i	−1.12143	+	0.647461i	−0.992516	−	2.64857i	−1.26506	−	2.19115i	−1.79103	+	4.18839i
43.12	−1.27678	−	0.608129i	−1.14865	−	0.663171i	1.26036	+	1.55290i			1.28693i	1.06328	+	1.54525i	3.60145	−	2.07930i	−0.664840	−	2.74918i	−0.620407	−	1.07458i	0.782619	−	1.64313i
43.13	−1.21210	+	0.728568i	2.61335	+	1.50882i	0.938379	−	1.76620i			0.755146i	−4.26692	+	0.0751615i	2.13122	−	1.23046i	0.149383	+	2.82448i	3.05306	+	5.28806i	−0.550175	−	0.915314i
43.14	−1.20341	+	0.742836i	−0.371524	−	0.214500i	0.896390	−	1.78787i		−	0.666498i	0.606434	−	0.0178505i	−1.08520	+	0.626541i	0.249370	+	2.81741i	−1.40798	−	2.43869i	0.495098	+	0.802070i
43.15	−1.20263	+	0.744103i	1.90164	+	1.09791i	0.892622	−	1.78976i			2.75390i	−3.10392	+	0.0946368i	−1.87485	+	1.08245i	0.258271	+	2.81661i	0.910822	+	1.57759i	−2.04919	−	3.31192i
43.16	−1.16505	−	0.801663i	1.14865	+	0.663171i	0.714672	+	1.86795i			1.28693i	−0.806588	−	1.69345i	3.60145	−	2.07930i	0.664840	−	2.74918i	−0.620407	−	1.07458i	1.03168	−	1.49933i
43.17	−1.13170	−	0.848088i	−0.593637	−	0.342737i	0.561494	+	1.91956i		−	3.22106i	0.381149	+	0.891332i	−1.12143	+	0.647461i	0.992516	−	2.64857i	−1.26506	−	2.19115i	−2.73174	+	3.64528i
43.18	−1.10302	−	0.885069i	−2.39320	−	1.38172i	0.433305	+	1.95250i		−	1.60862i	1.41683	+	3.64221i	0.824322	−	0.475923i	1.25015	−	2.53715i	2.31828	+	4.01537i	−1.42374	+	1.77434i
43.19	−1.02074	−	0.978820i	1.01294	+	0.584824i	0.0838224	+	1.99824i			1.81934i	−0.461516	−	1.58844i	−2.82002	+	1.62814i	1.87036	−	2.12173i	−0.815963	−	1.41329i	1.78080	−	1.85707i
43.20	−1.00832	+	0.991613i	1.38394	+	0.799017i	0.0334074	−	1.99972i		−	3.90803i	−2.18776	+	0.566668i	1.87027	−	1.07980i	1.94926	+	2.04948i	−0.223145	−	0.386499i	3.87525	+	3.94054i

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.e	even	6	1	inner
44.c	even	2	1	inner
52.i	odd	6	1	inner
143.i	odd	6	1	inner
572.s	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.s.a	✓	160
4.b	odd	2	1	inner	572.2.s.a	✓	160
11.b	odd	2	1	inner	572.2.s.a	✓	160
13.e	even	6	1	inner	572.2.s.a	✓	160
44.c	even	2	1	inner	572.2.s.a	✓	160
52.i	odd	6	1	inner	572.2.s.a	✓	160
143.i	odd	6	1	inner	572.2.s.a	✓	160
572.s	even	6	1	inner	572.2.s.a	✓	160

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
572.2.s.a	✓	160	1.a	even	1	1	trivial
572.2.s.a	✓	160	4.b	odd	2	1	inner
572.2.s.a	✓	160	11.b	odd	2	1	inner
572.2.s.a	✓	160	13.e	even	6	1	inner
572.2.s.a	✓	160	44.c	even	2	1	inner
572.2.s.a	✓	160	52.i	odd	6	1	inner
572.2.s.a	✓	160	143.i	odd	6	1	inner
572.2.s.a	✓	160	572.s	even	6	1	inner

Hecke kernels

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