Newform orbit 567.2.ba.a

• Label: 567.2.ba.a
• Level: $567$
• Weight: $2$
• Character orbit: 567.ba
• Analytic conductor: $4.528$
• Analytic rank: $0$
• Dimension: $132$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.ba (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.52751779461\)
Analytic rank:	\(0\)
Dimension:	\(132\)
Relative dimension:	\(22\) over \(\Q(\zeta_{18})\)
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
143.1	−1.75048	+	2.08614i		0		−0.940509	−	5.33389i	−2.08375	+	1.74847i		0		−0.122613	+	2.64291i	8.05677	+	4.65158i		0			−	7.40767i
143.2	−1.61592	+	1.92578i		0		−0.750127	−	4.25418i	2.10349	−	1.76504i		0		−0.122508	−	2.64291i	5.05050	+	2.91591i		0				6.90302i
143.3	−1.47978	+	1.76353i		0		−0.573000	−	3.24965i	1.41208	−	1.18487i		0		−2.40040	+	1.11270i	2.59137	+	1.49613i		0				4.24358i
143.4	−1.34473	+	1.60259i		0		−0.412694	−	2.34051i	−0.275976	+	0.231571i		0		2.18789	+	1.48767i	0.682329	+	0.393943i		0			−	0.753678i
143.5	−1.06515	+	1.26940i		0		−0.129525	−	0.734574i	2.93903	−	2.46614i		0		2.02233	+	1.70592i	−1.79971	−	1.03907i		0				6.35759i
143.6	−1.02575	+	1.22245i		0		−0.0949069	−	0.538244i	−1.45366	+	1.21977i		0		−2.50057	−	0.864386i	−2.00866	−	1.15970i		0			−	3.02821i
143.7	−0.905074	+	1.07862i		0		0.00302336	+	0.0171463i	−1.61655	+	1.35644i		0		1.08812	−	2.41164i	−2.46004	−	1.42030i		0			−	2.97133i
143.8	−0.594351	+	0.708320i		0		0.198832	+	1.12763i	0.386349	−	0.324185i		0		0.529787	−	2.59217i	−2.51844	−	1.45402i		0				0.466338i
143.9	−0.572822	+	0.682663i		0		0.209393	+	1.18753i	1.06212	−	0.891222i		0		−1.58403	+	2.11916i	−2.47415	−	1.42845i		0				1.23558i
143.10	−0.204899	+	0.244189i		0		0.329652	+	1.86955i	2.18935	−	1.83708i		0		0.468007	−	2.60403i	−1.07619	−	0.621337i		0				0.911030i
143.11	−0.00959490	+	0.0114348i		0		0.347258	+	1.96940i	−1.26073	+	1.05788i		0		1.81613	+	1.92397i	−0.0517058	−	0.0298524i		0			−	0.0245663i
143.12	0.0103898	−	0.0123821i		0		0.347251	+	1.96936i	−3.05823	+	2.56616i		0		−2.57348	+	0.614149i	0.0559891	+	0.0323253i		0				0.0645293i
143.13	0.159953	−	0.190625i		0		0.336544	+	1.90863i	−1.62936	+	1.36719i		0		2.64099	−	0.158668i	0.848674	+	0.489982i		0				0.529283i
143.14	0.575801	−	0.686212i		0		0.207955	+	1.17937i	−0.100696	+	0.0844942i		0		−1.70219	+	2.02548i	2.48059	+	1.43217i		0				0.117751i
143.15	0.582560	−	0.694268i		0		0.204665	+	1.16071i	0.931176	−	0.781349i		0		−2.06750	−	1.65089i	2.49483	+	1.44039i		0			−	1.10167i
143.16	0.720590	−	0.858766i		0		0.129068	+	0.731979i	3.14015	−	2.63490i		0		0.864922	+	2.50038i	2.66330	+	1.53766i		0			−	4.59533i
143.17	1.07972	−	1.28676i		0		−0.142658	−	0.809053i	−2.87107	+	2.40911i		0		−1.86335	−	1.87828i	1.71431	+	0.989760i		0				6.29553i
143.18	1.08992	−	1.29892i		0		−0.151961	−	0.861812i	−1.13756	+	0.954530i		0		2.51978	−	0.806679i	1.65184	+	0.953692i		0				2.51796i
143.19	1.22264	−	1.45709i		0		−0.280959	−	1.59339i	0.691544	−	0.580274i		0		−0.448602	+	2.60744i	0.629295	+	0.363324i		0			−	1.71711i
143.20	1.44973	−	1.72772i		0		−0.536009	−	3.03986i	2.61524	−	2.19445i		0		−0.126746	−	2.64271i	−2.12267	−	1.22552i		0			−	7.69979i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
189.ba	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	567.2.ba.a		132
3.b	odd	2	1		189.2.ba.a	✓	132
7.d	odd	6	1		567.2.bd.a		132
21.g	even	6	1		189.2.bd.a	yes	132
27.e	even	9	1		189.2.bd.a	yes	132
27.f	odd	18	1		567.2.bd.a		132
189.x	odd	18	1		189.2.ba.a	✓	132
189.ba	even	18	1	inner	567.2.ba.a		132

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
189.2.ba.a	✓	132	3.b	odd	2	1
189.2.ba.a	✓	132	189.x	odd	18	1
189.2.bd.a	yes	132	21.g	even	6	1
189.2.bd.a	yes	132	27.e	even	9	1
567.2.ba.a		132	1.a	even	1	1	trivial
567.2.ba.a		132	189.ba	even	18	1	inner
567.2.bd.a		132	7.d	odd	6	1
567.2.bd.a		132	27.f	odd	18	1

Hecke kernels

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