Newform orbit 945.2.cq.a

• Label: 945.2.cq.a
• Level: $945$
• Weight: $2$
• Character orbit: 945.cq
• Analytic conductor: $7.546$
• Analytic rank: $0$
• Dimension: $840$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cq (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.54586299101\)
Analytic rank:	\(0\)
Dimension:	\(840\)
Relative dimension:	\(140\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 840 q - 6 q^{4} - 9 q^{5} + 18 q^{6} + 6 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
59.1	−2.62775	−	0.956422i	1.62262	−	0.605890i	4.45823	+	3.74090i	1.70885	−	1.44216i	−4.84333	+	0.0402170i	−1.95692	+	1.78058i	−5.34084	−	9.25061i	2.26579	−	1.96626i	−5.86974	+	2.15526i
59.2	−2.60242	−	0.947203i	1.59382	+	0.678037i	4.34330	+	3.64446i	−2.19676	−	0.417403i	−3.50555	−	3.27421i	0.878479	−	2.49565i	−5.08159	−	8.80158i	2.08053	+	2.16134i	5.32153	+	3.16704i
59.3	−2.54534	−	0.926427i	−0.798901	+	1.53680i	4.08839	+	3.43057i	−2.22937	+	0.172982i	3.45721	−	3.17156i	0.437481	+	2.60933i	−4.51947	−	7.82795i	−1.72352	−	2.45550i	5.83475	+	1.62505i
59.4	−2.49720	−	0.908908i	−1.49632	−	0.872367i	3.87782	+	3.25388i	−0.684831	+	2.12862i	2.94372	+	3.53849i	2.62564	+	0.325623i	−4.06876	−	7.04730i	1.47795	+	2.61068i	3.64488	−	4.69314i
59.5	−2.47426	−	0.900558i	−0.916383	+	1.46978i	3.77888	+	3.17086i	2.20794	+	0.353584i	3.59099	−	2.81135i	−2.41070	−	1.09019i	−3.86135	−	6.68805i	−1.32048	−	2.69376i	−5.14459	−	2.86323i
59.6	−2.46902	−	0.898649i	−0.0368342	−	1.73166i	3.75639	+	3.15199i	−1.87108	+	1.22436i	−1.46521	+	4.30860i	−2.39691	−	1.12020i	−3.81459	−	6.60707i	−2.99729	+	0.127569i	5.72000	−	1.34154i
59.7	−2.46707	−	0.897939i	0.615215	+	1.61911i	3.74804	+	3.14498i	1.93318	+	1.12374i	−0.0639174	−	4.54687i	2.63285	+	0.260939i	−3.79726	−	6.57705i	−2.24302	+	1.99220i	−3.76024	−	4.50823i
59.8	−2.45697	−	0.894264i	−1.70185	+	0.322017i	3.70491	+	3.10879i	−0.788829	−	2.09231i	4.46937	+	0.730720i	0.250604	−	2.63386i	−3.70812	−	6.42265i	2.79261	−	1.09605i	0.0670548	+	5.84616i
59.9	−2.39200	−	0.870618i	−1.54526	−	0.782412i	3.43161	+	2.87947i	−1.19880	−	1.88756i	3.01509	+	3.21686i	−2.26978	+	1.35944i	−3.15600	−	5.46635i	1.77566	+	2.41806i	1.22418	+	5.55875i
59.10	−2.35969	−	0.858858i	−0.787423	−	1.54271i	3.29843	+	2.76771i	1.30003	−	1.81932i	0.533105	+	4.31662i	2.13650	+	1.56056i	−2.89507	−	5.01441i	−1.75993	+	2.42954i	−4.63021	+	3.17650i
59.11	−2.35489	−	0.857109i	0.787290	−	1.54278i	3.27877	+	2.75121i	2.03894	+	0.917995i	−3.17631	+	2.95828i	1.49462	−	2.18314i	−2.85702	−	4.94851i	−1.76035	−	2.42923i	−4.01466	−	3.90937i
59.12	−2.25854	−	0.822042i	0.947577	+	1.44986i	2.89317	+	2.42766i	−0.0181189	−	2.23599i	−0.948295	−	4.05352i	0.480457	+	2.60176i	−2.13521	−	3.69830i	−1.20420	+	2.74771i	−1.79716	+	5.06498i
59.13	−2.21151	−	0.804925i	1.46780	−	0.919545i	2.71080	+	2.27463i	−1.56034	+	1.60167i	−3.98622	+	0.852118i	−0.441816	+	2.60860i	−1.81062	−	3.13608i	1.30887	−	2.69942i	4.73994	−	2.28615i
59.14	−2.19932	−	0.800487i	1.26249	−	1.18580i	2.66414	+	2.23548i	−1.40865	−	1.73658i	−3.72583	+	1.59735i	2.63674	−	0.218146i	−1.72936	−	2.99533i	0.187754	−	2.99412i	1.70797	+	4.94690i
59.15	−2.19542	−	0.799069i	0.513011	+	1.65433i	2.64929	+	2.22302i	0.981646	−	2.00907i	0.195649	−	4.04190i	−1.29549	−	2.30688i	−1.70365	−	2.95080i	−2.47364	+	1.69738i	−3.76052	+	3.62636i
59.16	−2.18903	−	0.796741i	1.73141	+	0.0470493i	2.62496	+	2.20260i	0.718692	+	2.11742i	−3.75262	−	1.48248i	−1.55477	−	2.14072i	−1.66169	−	2.87814i	2.99557	+	0.162923i	0.113802	−	5.20771i
59.17	−2.18094	−	0.793796i	0.224921	−	1.71738i	2.59428	+	2.17686i	1.01687	+	1.99148i	−1.85379	+	3.56696i	0.0155159	+	2.64571i	−1.60908	−	2.78700i	−2.89882	−	0.772553i	−0.636893	−	5.15047i
59.18	−2.10971	−	0.767872i	−1.09141	+	1.34493i	2.32916	+	1.95440i	−0.303543	+	2.21537i	3.33529	−	1.99935i	1.44423	−	2.21680i	−1.16803	−	2.02308i	−0.617657	−	2.93573i	2.34151	−	4.44071i
59.19	−2.04032	−	0.742614i	−1.72420	+	0.164677i	2.07932	+	1.74476i	1.72468	+	1.42319i	3.64021	+	0.944427i	0.316859	+	2.62671i	−0.775533	−	1.34326i	2.94576	−	0.567872i	−2.46202	−	4.18453i
59.20	−2.02959	−	0.738710i	−0.867979	−	1.49887i	2.04145	+	1.71298i	−2.23336	+	0.109970i	0.654411	+	3.68327i	2.04659	−	1.67674i	−0.718063	−	1.24372i	−1.49322	+	2.60198i	4.61404	+	1.42661i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
189.bd	even	18	1	inner
945.cq	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	945.2.cq.a	yes	840
5.b	even	2	1	inner	945.2.cq.a	yes	840
7.d	odd	6	1		945.2.cl.a	✓	840
27.f	odd	18	1		945.2.cl.a	✓	840
35.i	odd	6	1		945.2.cl.a	✓	840
135.n	odd	18	1		945.2.cl.a	✓	840
189.bd	even	18	1	inner	945.2.cq.a	yes	840
945.cq	even	18	1	inner	945.2.cq.a	yes	840

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
945.2.cl.a	✓	840	7.d	odd	6	1
945.2.cl.a	✓	840	27.f	odd	18	1
945.2.cl.a	✓	840	35.i	odd	6	1
945.2.cl.a	✓	840	135.n	odd	18	1
945.2.cq.a	yes	840	1.a	even	1	1	trivial
945.2.cq.a	yes	840	5.b	even	2	1	inner
945.2.cq.a	yes	840	189.bd	even	18	1	inner
945.2.cq.a	yes	840	945.cq	even	18	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(945, [\chi])\).