Newform orbit 775.2.cx.a

• Label: 775.2.cx.a
• Level: $775$
• Weight: $2$
• Character orbit: 775.cx
• Analytic conductor: $6.188$
• Analytic rank: $0$
• Dimension: $1248$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.cx (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.

\(\operatorname{Tr}(f)(q) = \) \( 1248 q - 32 q^{2} - 24 q^{3} - 40 q^{4} - 8 q^{5} - 18 q^{6} - 4 q^{7} - 60 q^{8} - 10 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
37.1	−0.439468	−	2.77469i	−1.92350	+	0.100806i	−5.60368	+	1.82075i	1.90354	+	1.17326i	1.12502	+	5.29283i	0.893179	−	3.33339i	4.96388	+	9.74216i	0.706129	−	0.0742172i	2.41888	−	5.79735i
37.2	−0.429294	−	2.71046i	1.73215	−	0.0907781i	−5.26017	+	1.70913i	0.444385	−	2.19147i	−0.989652	−	4.65595i	0.350421	−	1.30779i	4.39897	+	8.63346i	0.00853774		0.000897353i	−6.13064	−	0.263703i
37.3	−0.411571	−	2.59856i	−1.88102	+	0.0985800i	−4.68098	+	1.52094i	1.00594	−	1.99702i	1.03034	+	4.84736i	−1.11042	+	4.14414i	3.48996	+	6.84944i	0.544944	−	0.0572759i	−5.60338	−	1.79207i
37.4	−0.410948	−	2.59463i	0.303289	−	0.0158947i	−4.66110	+	1.51448i	−2.19328	−	0.435366i	−0.165877	−	0.780389i	−0.0496794	+	0.185406i	3.45975	+	6.79013i	−2.89183	+	0.303944i	−0.228288	+	5.86964i
37.5	−0.409274	−	2.58406i	1.73053	−	0.0906933i	−4.60773	+	1.49714i	0.694877	+	2.12536i	−0.942619	−	4.43468i	−0.142807	+	0.532961i	3.37901	+	6.63168i	0.00294942		0.000309996i	5.20765	−	2.66546i
37.6	−0.384587	−	2.42819i	2.88397	−	0.151142i	−3.84607	+	1.24966i	−1.82254	+	1.29551i	−1.47614	−	6.94469i	0.566986	−	2.11602i	2.28133	+	4.47737i	5.31087	−	0.558195i	3.84666	+	3.92723i
37.7	−0.369931	−	2.33565i	−2.71641	+	0.142361i	−3.41631	+	1.11003i	−0.267936	+	2.21996i	1.33739	+	6.29193i	−0.561026	+	2.09378i	1.70927	+	3.35462i	4.37506	−	0.459837i	5.28416	−	0.195425i
37.8	−0.363976	−	2.29806i	−0.808757	+	0.0423852i	−3.24647	+	1.05484i	−1.28860	+	1.82743i	0.391772	+	1.84314i	0.985045	−	3.67624i	1.49313	+	2.93043i	−2.33127	+	0.245027i	4.66856	+	2.29614i
37.9	−0.360664	−	2.27714i	3.04220	−	0.159435i	−3.15319	+	1.02453i	2.10073	−	0.766119i	−1.46027	−	6.87003i	−1.06792	+	3.98552i	1.37688	+	2.70228i	6.24602	−	0.656483i	−2.50222	−	4.50735i
37.10	−0.357243	−	2.25554i	−1.43377	+	0.0751408i	−3.05774	+	0.993521i	−1.95306	−	1.08883i	0.681688	+	3.20709i	0.273833	−	1.02196i	1.25977	+	2.47243i	−0.933512	+	0.0981161i	−1.75817	+	4.79420i
37.11	−0.349860	−	2.20893i	−0.468485	+	0.0245523i	−2.85485	+	0.927596i	2.17849	+	0.504156i	0.218138	+	1.02626i	−0.769615	+	2.87224i	1.01712	+	1.99622i	−2.76469	+	0.290581i	0.351478	−	4.98852i
37.12	−0.322919	−	2.03883i	0.500390	−	0.0262243i	−2.15044	+	0.698722i	1.46544	−	1.68893i	−0.215052	−	1.01174i	1.10275	−	4.11552i	0.244700	+	0.480250i	−2.73386	+	0.287341i	−3.91666	−	2.44240i
37.13	−0.322799	−	2.03807i	1.19891	−	0.0628322i	−2.14743	+	0.697743i	−1.47135	−	1.68378i	−0.515064	−	2.42319i	−0.647724	+	2.41734i	0.241643	+	0.474250i	−1.55013	+	0.162925i	−2.95673	+	3.54224i
37.14	−0.317113	−	2.00217i	0.235593	−	0.0123469i	−2.00603	+	0.651799i	2.23598	+	0.0193585i	−0.0994303	−	0.467783i	0.456415	−	1.70336i	0.100556	+	0.197353i	−2.92821	+	0.307768i	−0.670301	−	4.48297i
37.15	−0.309400	−	1.95347i	−2.36856	+	0.124131i	−1.81822	+	0.590776i	0.275683	−	2.21901i	0.975318	+	4.58851i	0.128476	−	0.479478i	−0.0792051	−	0.155449i	2.61109	−	0.274437i	−4.42007	+	0.148021i
37.16	−0.307697	−	1.94272i	−3.21364	+	0.168420i	−1.77739	+	0.577509i	2.04738	−	0.899030i	1.31602	+	6.19139i	0.515241	−	1.92290i	−0.117106	−	0.229834i	7.31552	−	0.768892i	−2.37654	−	3.70086i
37.17	−0.298300	−	1.88339i	3.00597	−	0.157536i	−1.55608	+	0.505600i	−0.495430	−	2.18049i	−1.19338	−	5.61443i	0.817934	−	3.05257i	−0.314981	−	0.618185i	6.02748	−	0.633513i	−3.95894	+	1.58353i
37.18	−0.285286	−	1.80122i	−1.78983	+	0.0938013i	−1.26090	+	0.409691i	−1.62788	+	1.53297i	0.679571	+	3.19713i	−0.387178	+	1.44497i	−0.558200	−	1.09553i	0.211144	−	0.0221922i	3.22563	+	2.49485i
37.19	−0.281058	−	1.77453i	1.96097	−	0.102770i	−1.16786	+	0.379460i	−1.94291	+	1.10684i	−0.733515	−	3.45092i	−1.23184	+	4.59728i	−0.629726	−	1.23591i	0.851270	−	0.0894721i	2.51019	+	3.13667i
37.20	−0.252215	−	1.59242i	2.44563	−	0.128170i	−0.570089	+	0.185233i	1.91791	+	1.14962i	−0.820927	−	3.86216i	0.490554	−	1.83077i	−1.02516	−	2.01199i	2.98112	−	0.313328i	1.34696	−	3.34407i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
25.f	odd	20	1	inner
31.e	odd	6	1	inner
775.cx	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.cx.a	✓	1248
25.f	odd	20	1	inner	775.2.cx.a	✓	1248
31.e	odd	6	1	inner	775.2.cx.a	✓	1248
775.cx	even	60	1	inner	775.2.cx.a	✓	1248

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
775.2.cx.a	✓	1248	1.a	even	1	1	trivial
775.2.cx.a	✓	1248	25.f	odd	20	1	inner
775.2.cx.a	✓	1248	31.e	odd	6	1	inner
775.2.cx.a	✓	1248	775.cx	even	60	1	inner

Hecke kernels

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