Newform orbit 667.2.o.a

• Label: 667.2.o.a
• Level: $667$
• Weight: $2$
• Character orbit: 667.o
• Analytic conductor: $5.326$
• Analytic rank: $0$
• Dimension: $72$
• CM discriminant: -23
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.o (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.32602181482\)
Analytic rank:	\(0\)
Dimension:	\(72\)
Relative dimension:	\(6\) over \(\Q(\zeta_{28})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{28}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 72 q - 18 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
68.1	−1.87341	+	1.17714i	1.36096	+	0.476221i	1.25623	−	2.60858i		0		−3.11021	+	0.709885i		0		0.221790	+	1.96844i	−0.720065	−	0.574233i		0
68.2	−1.75667	+	1.10379i	3.22307	+	1.12780i	0.999782	−	2.07607i		0		−6.90674	+	1.57642i		0		0.0706769	+	0.627275i	6.77076	+	5.39950i		0
68.3	−0.531351	+	0.333870i	−2.08809	−	0.730654i	−0.696903	+	1.44713i		0		1.35345	−	0.308917i		0		−0.253378	−	2.24879i	1.48076	+	1.18087i		0
68.4	−0.355355	+	0.223284i	−3.25518	−	1.13904i	−0.791346	+	1.64325i		0		1.41107	−	0.322069i		0		−0.179682	−	1.59472i	6.95330	+	5.54507i		0
68.5	2.22876	−	1.40042i	1.89422	+	0.662816i	2.13842	−	4.44048i		0		5.14999	−	1.17545i		0		−0.863090	−	7.66014i	0.803247	+	0.640568i		0
68.6	2.28803	−	1.43766i	−1.13498	−	0.397148i	2.30042	−	4.77688i		0		−3.16783	+	0.723037i		0		−0.999005	−	8.86641i	−1.21503	−	0.968958i		0
114.1	−0.308696	+	2.73975i	−1.78847	+	2.84633i	−5.46111	−	1.24646i		0		−7.24615	−	5.77861i		0		3.27960	−	9.37257i	−3.60132	−	7.47822i		0
114.2	−0.285230	+	2.53148i	1.84266	−	2.93258i	−4.37720	−	0.999068i		0		6.89820	+	5.50113i		0		2.09486	−	5.98676i	−3.90297	−	8.10461i		0
114.3	0.0234543	−	0.208163i	−0.890209	+	1.41676i	1.90707	+	0.435277i		0		0.274037	+	0.218538i		0		0.273711	−	0.782222i	0.0869151	+	0.180481i		0
114.4	0.0931414	−	0.826653i	0.508794	−	0.809741i	1.27518	+	0.291051i		0		−0.621985	−	0.496017i		0		0.908877	−	2.59742i	0.904842	+	1.87892i		0
114.5	0.215555	−	1.91310i	1.27967	−	2.03659i	−1.66364	−	0.379715i		0		−3.62036	−	2.88714i		0		0.186673	−	0.533482i	−1.20847	−	2.50942i		0
114.6	0.261775	−	2.32332i	−0.952454	+	1.51582i	−3.37944	−	0.771335i		0		3.27241	+	2.60966i		0		−1.13231	+	3.23597i	−0.0888947	−	0.184592i		0
137.1	−0.869823	+	2.48581i	−1.07859	−	0.121528i	−3.85900	−	3.07745i		0		1.24028	−	2.57546i		0		6.54674	−	4.11359i	−1.77620	−	0.405406i		0
137.2	−0.467627	+	1.33640i	2.88145	+	0.324661i	−0.00362845	−	0.00289360i		0		−1.78132	+	3.69895i		0		−2.39211	+	1.50306i	5.27256	+	1.20343i		0
137.3	−0.466543	+	1.33330i	0.190262	+	0.0214374i	0.00362565	+	0.00289136i		0		−0.117348	+	0.243676i		0		−2.39767	+	1.50655i	−2.88904	−	0.659405i		0
137.4	0.139849	−	0.399667i	−2.29172	−	0.258215i	1.42349	+	1.13519i		0		−0.423696	+	0.879814i		0		1.36983	−	0.860719i	2.26054	+	0.515953i		0
137.5	0.729974	−	2.08614i	3.37031	+	0.379743i	−2.25547	−	1.79868i		0		3.25244	−	6.75376i		0		−1.65593	+	1.04049i	8.29001	+	1.89214i		0
137.6	0.934170	−	2.66970i	−3.07171	−	0.346099i	−4.69099	−	3.74094i		0		−3.79348	+	7.87725i		0		−9.57958	+	6.01925i	6.39084	+	1.45867i		0
160.1	−2.68633	+	0.302676i	−2.81915	+	1.77139i	5.17489	−	1.18113i		0		7.03701	−	5.61183i		0		−8.44070	+	2.95353i	3.50814	−	7.28474i		0
160.2	−1.58174	+	0.178219i	2.51109	−	1.57782i	0.520271	−	0.118748i		0		−3.69069	+	2.94323i		0		2.20307	−	0.770889i	2.51441	−	5.22122i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.b	odd	2	1	CM by \(\Q(\sqrt{-23}) \)
29.f	odd	28	1	inner
667.o	even	28	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	667.2.o.a	✓	72
23.b	odd	2	1	CM	667.2.o.a	✓	72
29.f	odd	28	1	inner	667.2.o.a	✓	72
667.o	even	28	1	inner	667.2.o.a	✓	72

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
667.2.o.a	✓	72	1.a	even	1	1	trivial
667.2.o.a	✓	72	23.b	odd	2	1	CM
667.2.o.a	✓	72	29.f	odd	28	1	inner
667.2.o.a	✓	72	667.o	even	28	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^72 + 6*T2^69 - 72*T2^68 + 36*T2^67 - 31*T2^66 - 648*T2^65 + 4488*T2^64 - 4224*T2^63 + 1584*T2^62 - 11232*T2^61 - 273306*T2^60 + 345384*T2^59 - 429000*T2^58 + 957924*T2^57 + 14445036*T2^56 - 4503816*T2^55 + 41704886*T2^54 - 46701360*T2^53 - 656232936*T2^52 + 259381962*T2^51 + 526437180*T2^50 + 3940008192*T2^49 + 30512384645*T2^48 - 6627555000*T2^47 - 65472633936*T2^46 - 114216168240*T2^45 - 680635479168*T2^44 + 68409939924*T2^43 + 4258361050169*T2^42 + 4708110028176*T2^41 + 15206519515056*T2^40 + 4968833434812*T2^39 - 69718818270888*T2^38 - 200166278572944*T2^37 - 290307277727672*T2^36 - 233421103209816*T2^35 + 521268033975264*T2^34 + 1821924724747068*T2^33 + 5328987121381068*T2^32 + 7383417734309328*T2^31 + 611520496887113*T2^30 - 7829667345042864*T2^29 - 51614821411386624*T2^28 - 82577720636255568*T2^27 - 43858882943525196*T2^26 + 126970725784193748*T2^25 + 531579049540912549*T2^24 + 584027380692664056*T2^23 + 264509293709721168*T2^22 - 306377404053478422*T2^21 - 672135122465712432*T2^20 - 105656979627310752*T2^19 + 92455524270775894*T2^18 + 283606637471868888*T2^17 + 365562648973863720*T2^16 + 314825688507514308*T2^15 + 436827414133604160*T2^14 - 23266281455953128*T2^13 + 75292100831616166*T2^12 - 67106605549164048*T2^11 - 143950231610794392*T2^10 - 76482219283187424*T2^9 + 24425877191288832*T2^8 + 5546104946095392*T2^7 + 4849506639716529*T2^6 + 4244202570940416*T2^5 + 1812670065523464*T2^4 + 96008613211014*T2^3 + 79470656197128*T2^2 + 283285404612*T2 + 283888801