Newform orbit 775.2.cu.a

• Label: 775.2.cu.a
• Level: $775$
• Weight: $2$
• Character orbit: 775.cu
• Analytic conductor: $6.188$
• Analytic rank: $0$
• Dimension: $1248$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.cu (of order \(60\), degree \(16\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.18840615665\)
Analytic rank:	\(0\)
Dimension:	\(1248\)
Relative dimension:	\(78\) over \(\Q(\zeta_{60})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1248 q - 12 q^{2} - 14 q^{3} - 8 q^{5} - 18 q^{6} - 14 q^{7} - 30 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
13.1	−1.93571	+	1.93571i	2.78853	+	0.146140i		−	5.49394i	−0.823875	+	2.07876i	−5.68066	+	5.11489i	−2.45503	−	0.128663i	6.76326	+	6.76326i	4.77096	+	0.501448i	−2.42909	−	5.61865i
13.2	−1.93330	+	1.93330i	1.38204	+	0.0724297i		−	5.47528i	1.20543	−	1.88333i	−2.81193	+	2.53187i	−0.830345	−	0.0435165i	6.71874	+	6.71874i	−1.07877	−	0.113384i	1.31059	+	5.97149i
13.3	−1.88031	+	1.88031i	−0.338391	−	0.0177343i		−	5.07112i	1.59029	+	1.57193i	0.669626	−	0.602934i	−2.16039	−	0.113221i	5.77466	+	5.77466i	−2.86937	−	0.301583i	−5.94596	+	0.0345244i
13.4	−1.87877	+	1.87877i	−2.51966	−	0.132050i		−	5.05953i	−2.18674	+	0.467065i	4.98194	−	4.48576i	−1.84510	−	0.0966976i	5.74813	+	5.74813i	3.34767	+	0.351854i	3.23088	−	4.98589i
13.5	−1.87315	+	1.87315i	−0.0103255		0.000541138i		−	5.01739i	−2.21766	−	0.286356i	0.0203549	−	0.0183277i	2.92819	+	0.153460i	5.65203	+	5.65203i	−2.98346	−	0.313574i	4.69039	−	3.61762i
13.6	−1.79275	+	1.79275i	−2.33916	−	0.122590i		−	4.42790i	1.64182	−	1.51804i	4.41329	−	3.97375i	5.00171	+	0.262129i	4.35262	+	4.35262i	2.47306	+	0.259929i	−0.221901	+	5.66483i
13.7	−1.68823	+	1.68823i	2.05493	+	0.107694i		−	3.70024i	1.88839	+	1.19749i	−3.65100	+	3.28738i	4.37650	+	0.229363i	2.87039	+	2.87039i	1.22756	+	0.129022i	−5.20967	+	1.16641i
13.8	−1.65902	+	1.65902i	−1.52606	−	0.0799776i		−	3.50469i	2.15248	−	0.605659i	2.66445	−	2.39908i	−2.70742	−	0.141890i	2.49631	+	2.49631i	−0.661094	−	0.0694838i	−2.56621	+	4.57581i
13.9	−1.65836	+	1.65836i	−2.78264	−	0.145832i		−	3.50033i	0.410322	+	2.19810i	4.85646	−	4.37278i	0.865987	+	0.0453845i	2.48810	+	2.48810i	4.73824	+	0.498009i	−4.32571	−	2.96478i
13.10	−1.61574	+	1.61574i	3.44659	+	0.180628i		−	3.22126i	0.490217	−	2.18167i	−5.86066	+	5.27696i	1.23122	+	0.0645255i	1.97324	+	1.97324i	8.86280	+	0.931518i	2.73296	+	4.31709i
13.11	−1.60009	+	1.60009i	1.73691	+	0.0910278i		−	3.12055i	−1.93511	−	1.12043i	−2.92486	+	2.63356i	−3.90664	−	0.204738i	1.79298	+	1.79298i	0.0250161	+	0.00262929i	4.88912	−	1.30356i
13.12	−1.56153	+	1.56153i	0.770943	+	0.0404034i		−	2.87675i	0.0511398	−	2.23548i	−1.26694	+	1.14076i	0.452922	+	0.0237367i	1.36907	+	1.36907i	−2.39085	−	0.251288i	3.41092	+	3.57063i
13.13	−1.45119	+	1.45119i	0.656856	+	0.0344244i		−	2.21190i	−1.06498	+	1.96617i	−1.00318	+	0.903266i	0.0584439	+	0.00306292i	0.307505	+	0.307505i	−2.55329	−	0.268362i	−1.30779	−	4.39877i
13.14	−1.41978	+	1.41978i	−2.59641	−	0.136072i		−	2.03152i	−0.437461	−	2.19286i	3.87951	−	3.49312i	−2.85016	−	0.149371i	0.0447554	+	0.0447554i	3.73926	+	0.393012i	3.73446	+	2.49227i
13.15	−1.38309	+	1.38309i	2.61376	+	0.136981i		−	1.82586i	−1.78534	+	1.34632i	−3.80452	+	3.42560i	3.55014	+	0.186055i	−0.240847	−	0.240847i	3.82941	+	0.402488i	0.607208	−	4.33135i
13.16	−1.34036	+	1.34036i	−0.816356	−	0.0427834i		−	1.59313i	−1.76895	−	1.36777i	1.15156	−	1.03687i	2.18314	+	0.114414i	−0.545356	−	0.545356i	−2.31896	−	0.243732i	4.20434	−	0.537729i
13.17	−1.26007	+	1.26007i	−1.17562	−	0.0616116i		−	1.17556i	−2.02454	+	0.949331i	1.55900	−	1.40373i	−4.40056	−	0.230623i	−1.03885	−	1.03885i	−1.60528	−	0.168722i	1.35484	−	3.74729i
13.18	−1.17086	+	1.17086i	−0.621824	−	0.0325884i		−	0.741839i	1.35435	+	1.77925i	0.766227	−	0.689914i	−2.99541	−	0.156983i	−1.47313	−	1.47313i	−2.59796	−	0.273057i	−3.66902	−	0.497495i
13.19	−1.13310	+	1.13310i	−0.129870	−	0.00680622i		−	0.567816i	2.23519	−	0.0627536i	0.154868	−	0.139444i	3.79209	+	0.198735i	−1.62280	−	1.62280i	−2.96675	−	0.311818i	−2.46158	+	2.60379i
13.20	−1.12379	+	1.12379i	2.18667	+	0.114599i		−	0.525791i	0.763567	+	2.10166i	−2.58613	+	2.32857i	−2.07664	−	0.108832i	−1.65670	−	1.65670i	1.78483	+	0.187593i	−3.21990	−	1.50373i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
775.cu	even	60	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	775.2.cu.a	✓	1248
25.f	odd	20	1		775.2.cy.a	yes	1248
31.h	odd	30	1		775.2.cy.a	yes	1248
775.cu	even	60	1	inner	775.2.cu.a	✓	1248

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
775.2.cu.a	✓	1248	1.a	even	1	1	trivial
775.2.cu.a	✓	1248	775.cu	even	60	1	inner
775.2.cy.a	yes	1248	25.f	odd	20	1
775.2.cy.a	yes	1248	31.h	odd	30	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(775, [\chi])\).