Newform orbit 567.2.u.a

• Label: 567.2.u.a
• Level: $567$
• Weight: $2$
• Character orbit: 567.u
• 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.u (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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
100.1	−0.456041	+	2.58633i		0		−4.60177	−	1.67491i	−2.97048	−	1.08117i		0		−2.55032	+	0.704184i	3.80423	−	6.58912i		0		4.15092	−	7.18961i
100.2	−0.427861	+	2.42652i		0		−3.82554	−	1.39238i	2.97164	+	1.08159i		0		0.768747	−	2.53161i	2.55149	−	4.41931i		0		−3.89594	+	6.74796i
100.3	−0.373934	+	2.12069i		0		−2.47810	−	0.901956i	1.18205	+	0.430229i		0		−2.62839	+	0.302569i	0.686013	−	1.18821i		0		−1.35439	+	2.34587i
100.4	−0.371090	+	2.10456i		0		−2.41207	−	0.877922i	−2.18602	−	0.795646i		0		1.27150	+	2.32019i	0.605711	−	1.04912i		0		2.48569	−	4.30535i
100.5	−0.340870	+	1.93317i		0		−1.74157	−	0.633879i	−1.35943	−	0.494793i		0		−0.147009	−	2.64166i	−0.143948	+	0.249325i		0		1.41991	−	2.45935i
100.6	−0.246187	+	1.39619i		0		−0.00936568	−	0.00340883i	−3.04103	−	1.10685i		0		1.78778	−	1.95034i	−1.41067	+	2.44335i		0		2.29403	−	3.97338i
100.7	−0.241593	+	1.37014i		0		0.0604707	+	0.0220095i	1.40760	+	0.512324i		0		1.17416	+	2.37094i	−1.43604	+	2.48730i		0		−1.04202	+	1.80483i
100.8	−0.101938	+	0.578121i		0		1.55555	+	0.566175i	3.06658	+	1.11614i		0		−1.48906	−	2.18694i	−1.07293	+	1.85836i		0		−0.957867	+	1.65908i
100.9	−0.0954712	+	0.541444i		0		1.59534	+	0.580656i	0.969531	+	0.352880i		0		2.17686	+	1.50376i	−1.01650	+	1.76063i		0		−0.283627	+	0.491257i
100.10	−0.0570934	+	0.323793i		0		1.77780	+	0.647067i	−1.85642	−	0.675680i		0		−2.33644	+	1.24140i	−0.639805	+	1.10817i		0		0.324770	−	0.562517i
100.11	−0.0290601	+	0.164808i		0		1.85307	+	0.674462i	0.999212	+	0.363683i		0		1.97858	−	1.75648i	−0.332357	+	0.575660i		0		−0.0889751	+	0.154109i
100.12	0.0305699	−	0.173370i		0		1.85026	+	0.673440i	−2.52551	−	0.919210i		0		−1.78991	+	1.94839i	0.349362	−	0.605113i		0		−0.236568	+	0.409748i
100.13	0.134854	−	0.764795i		0		1.31266	+	0.477769i	−1.10529	−	0.402293i		0		−0.975813	−	2.45923i	1.31901	−	2.28459i		0		−0.456725	+	0.791071i
100.14	0.165988	−	0.941364i		0		1.02077	+	0.371530i	2.75749	+	1.00364i		0		0.0940141	+	2.64408i	1.47507	−	2.55489i		0		1.40250	−	2.42921i
100.15	0.203963	−	1.15673i		0		0.582964	+	0.212181i	3.41115	+	1.24156i		0		−1.99948	−	1.73265i	1.53891	−	2.66548i		0		2.13189	−	3.69255i
100.16	0.266701	−	1.51254i		0		−0.337258	−	0.122752i	−3.71318	−	1.35149i		0		2.56740	−	0.639091i	1.26026	−	2.18283i		0		−3.03449	+	5.25589i
100.17	0.279530	−	1.58529i		0		−0.555633	−	0.202234i	−0.230811	−	0.0840085i		0		−1.31413	+	2.29631i	1.13383	−	1.96386i		0		−0.197697	+	0.342421i
100.18	0.310937	−	1.76341i		0		−1.13356	−	0.412582i	0.00172074		0.000626297i		0		2.59651	−	0.508047i	0.710598	−	1.23079i		0		0.00163946	−	0.00283963i
100.19	0.324131	−	1.83824i		0		−1.39467	−	0.507617i	−1.37479	−	0.500384i		0		−2.42382	−	1.06071i	0.481419	−	0.833843i		0		−1.36544	+	2.36501i
100.20	0.422628	−	2.39684i		0		−3.68685	−	1.34190i	2.38847	+	0.869333i		0		2.35689	+	1.20212i	−2.34068	+	4.05418i		0		3.09309	−	5.35738i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
189.u	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.u.a		132
3.b	odd	2	1		189.2.u.a	✓	132
7.c	even	3	1		567.2.w.a		132
21.h	odd	6	1		189.2.w.a	yes	132
27.e	even	9	1		567.2.w.a		132
27.f	odd	18	1		189.2.w.a	yes	132
189.u	even	9	1	inner	567.2.u.a		132
189.bc	odd	18	1		189.2.u.a	✓	132

    

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

Hecke kernels

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