Newform orbit 567.2.w.a

• Label: 567.2.w.a
• Level: $567$
• Weight: $2$
• Character orbit: 567.w
• Analytic conductor: $4.528$
• Analytic rank: $0$
• Dimension: $132$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.w (of order \(9\), degree \(6\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.52751779461\)
Analytic rank:	\(0\)
Dimension:	\(132\)
Relative dimension:	\(22\) over \(\Q(\zeta_{9})\)
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
37.1	−0.475852	−	2.69869i		0		−5.17712	+	1.88432i	−0.0114982	+	0.0652096i		0		2.53330	+	0.763145i	4.80842	+	8.32842i		0		0.181452
37.2	−0.442261	−	2.50819i		0		−4.21603	+	1.53451i	0.331479	−	1.87991i		0		0.0136229	−	2.64572i	3.16655	+	5.48462i		0		−4.86178
37.3	−0.379821	−	2.15407i		0		−2.61637	+	0.952279i	0.347563	−	1.97113i		0		0.0877467	+	2.64430i	0.857725	+	1.48562i		0		−4.37795
37.4	−0.351787	−	1.99508i		0		−1.97722	+	0.719650i	−0.155052	+	0.879341i		0		−1.72949	+	2.00222i	0.105462	+	0.182666i		0		1.80890
37.5	−0.337831	−	1.91594i		0		−1.67729	+	0.610485i	−0.582582	+	3.30399i		0		0.666452	−	2.56044i	−0.209199	−	0.362343i		0		6.52704
37.6	−0.306313	−	1.73719i		0		−1.04461	+	0.380207i	0.723302	−	4.10205i		0		−1.55501	−	2.14055i	−0.783518	−	1.35709i		0		−7.34759
37.7	−0.278319	−	1.57843i		0		−0.534587	+	0.194574i	−0.620906	+	3.52133i		0		−2.64260	+	0.129178i	−1.14687	−	1.98644i		0		5.73098
37.8	−0.162199	−	0.919879i		0		1.05952	−	0.385633i	0.120368	−	0.682641i		0		1.39323	−	2.24920i	−1.46066	−	2.52993i		0		−0.647471
37.9	−0.161602	−	0.916488i		0		1.06555	−	0.387829i	−0.260888	+	1.47957i		0		1.80008	+	1.93899i	−1.45826	−	2.52578i		0		1.39817
37.10	−0.0910389	−	0.516307i		0		1.62110	−	0.590032i	−0.0290567	+	0.164789i		0		−0.352779	+	2.62213i	−0.976493	−	1.69134i		0		0.0877269
37.11	−0.0119703	−	0.0678870i		0		1.87492	−	0.682415i	−0.115724	+	0.656302i		0		−1.45670	−	2.20863i	−0.137705	−	0.238512i		0		0.0459397
37.12	0.000974390		0.00552604i		0		1.87936	−	0.684030i	0.601605	−	3.41187i		0		2.41288	−	1.08535i	0.0112225	+	0.0194379i		0		0.0194403
37.13	0.0572325	+	0.324581i		0		1.77731	−	0.646887i	0.607976	−	3.44800i		0		−2.50814	+	0.842165i	0.641276	+	1.11072i		0		1.15395
37.14	0.162149	+	0.919594i		0		1.06003	−	0.385818i	−0.575026	+	3.26114i		0		1.06445	+	2.42218i	1.46046	+	2.52959i		0		−3.09216
37.15	0.177652	+	1.00751i		0		0.895865	−	0.326068i	−0.356801	+	2.02352i		0		−2.48566	+	0.906357i	1.51072	+	2.61665i		0		−2.10210
37.16	0.199381	+	1.13075i		0		0.640547	−	0.233140i	0.0295570	−	0.167626i		0		−1.82867	−	1.91206i	1.53953	+	2.66654i		0		0.195436
37.17	0.202689	+	1.14951i		0		0.599102	−	0.218055i	0.490607	−	2.78237i		0		2.49252	+	0.887321i	1.53933	+	2.66619i		0		3.29779
37.18	0.303930	+	1.72367i		0		−0.999292	+	0.363713i	−0.0231991	+	0.131569i		0		1.74352	−	1.99001i	0.819627	+	1.41964i		0		−0.233833
37.19	0.345866	+	1.96151i		0		−1.84850	+	0.672798i	−0.424474	+	2.40731i		0		2.63001	+	0.288173i	0.0327363	+	0.0567010i		0		−4.86876
37.20	0.402178	+	2.28086i		0		−3.16120	+	1.15058i	−0.125418	+	0.711279i		0		−2.42560	+	1.05663i	−1.57964	−	2.73601i		0		−1.67277

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
189.w	even	9	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	567.2.w.a		132
3.b	odd	2	1		189.2.w.a	yes	132
7.c	even	3	1		567.2.u.a		132
21.h	odd	6	1		189.2.u.a	✓	132
27.e	even	9	1		567.2.u.a		132
27.f	odd	18	1		189.2.u.a	✓	132
189.w	even	9	1	inner	567.2.w.a		132
189.bf	odd	18	1		189.2.w.a	yes	132

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
189.2.u.a	✓	132	21.h	odd	6	1
189.2.u.a	✓	132	27.f	odd	18	1
189.2.w.a	yes	132	3.b	odd	2	1
189.2.w.a	yes	132	189.bf	odd	18	1
567.2.u.a		132	7.c	even	3	1
567.2.u.a		132	27.e	even	9	1
567.2.w.a		132	1.a	even	1	1	trivial
567.2.w.a		132	189.w	even	9	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(567, [\chi])\).