Newform orbit 483.2.u.a

• Label: 483.2.u.a
• Level: $483$
• Weight: $2$
• Character orbit: 483.u
• Analytic conductor: $3.857$
• Analytic rank: $0$
• Dimension: $480$
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$483 = 3 \cdot 7 \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	483.u (of order $22$, degree $10$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

$\operatorname{Tr}(f)(q) =$ 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

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	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
113.1	−1.50106	+	2.33570i	0.521192	−	1.65177i	−2.37146	−	5.19277i	−1.06257	−	0.311999i	3.07570	+	3.69676i	0.755750	+	0.654861i	10.1921	+	1.46540i	−2.45672	−	1.72178i	2.32371	−	2.01351i
113.2	−1.48162	+	2.30545i	−0.121691	+	1.72777i	−2.28907	−	5.01236i	−4.08876	−	1.20057i	−3.80299	−	2.84046i	−0.755750	−	0.654861i	9.52207	+	1.36907i	−2.97038	−	0.420508i	8.82585	−	7.64764i
113.3	−1.39817	+	2.17560i	1.72494	+	0.156831i	−1.94751	−	4.26445i	1.23964	+	0.363993i	−2.75296	+	3.53349i	−0.755750	−	0.654861i	6.88105	+	0.989346i	2.95081	+	0.541047i	−2.52514	+	2.18804i
113.4	−1.39646	+	2.17293i	−1.51591	+	0.837856i	−1.94070	−	4.24954i	3.72219	+	1.09293i	0.296307	−	4.46400i	−0.755750	−	0.654861i	6.83069	+	0.982105i	1.59599	−	2.54024i	−7.57275	+	6.56182i
113.5	−1.33937	+	2.08410i	−1.69763	−	0.343591i	−1.71873	−	3.76350i	−1.11280	−	0.326747i	2.98983	−	3.07784i	0.755750	+	0.654861i	5.24122	+	0.753574i	2.76389	+	1.16658i	2.17142	−	1.88155i
113.6	−1.30013	+	2.02305i	−0.657657	−	1.60234i	−1.57155	−	3.44121i	1.14892	+	0.337353i	4.09665	+	0.752782i	−0.755750	−	0.654861i	4.24430	+	0.610238i	−2.13497	+	2.10758i	−2.17623	+	1.88572i
113.7	−1.20683	+	1.87786i	1.44817	+	0.950153i	−1.23910	−	2.71324i	−0.604163	−	0.177398i	−3.53195	+	1.57280i	0.755750	+	0.654861i	2.17147	+	0.312210i	1.19442	+	2.75197i	1.06225	−	0.920445i
113.8	−1.18675	+	1.84662i	−1.11165	+	1.32824i	−1.17080	−	2.56370i	−0.291860	−	0.0856978i	−1.13351	−	3.62910i	0.755750	+	0.654861i	1.77815	+	0.255660i	−0.528462	−	2.95309i	0.504617	−	0.437253i
113.9	−1.07812	+	1.67759i	1.58707	−	0.693695i	−0.821124	−	1.79801i	−1.95772	−	0.574839i	−0.547316	+	3.41033i	−0.755750	−	0.654861i	−0.0461173	−	0.00663067i	2.03757	−	2.20188i	3.07500	−	2.66450i
113.10	−1.07128	+	1.66695i	−1.25731	−	1.19129i	−0.800245	−	1.75229i	3.65018	+	1.07179i	3.33276	−	0.819664i	0.755750	+	0.654861i	−0.144404	−	0.0207621i	0.161658	+	2.99564i	−5.69700	+	4.93648i
113.11	−1.06610	+	1.65888i	−0.893651	−	1.48371i	−0.784489	−	1.71779i	−3.45226	−	1.01367i	3.41401	+	0.0993161i	−0.755750	−	0.654861i	−0.217736	−	0.0313058i	−1.40277	+	2.65183i	5.36201	−	4.64621i
113.12	−0.908799	+	1.41412i	1.31791	−	1.12388i	−0.342987	−	0.751037i	−2.80823	−	0.824571i	0.391583	+	2.88507i	0.755750	+	0.654861i	−1.95395	−	0.280936i	0.473786	−	2.96235i	3.71816	−	3.22180i
113.13	−0.853002	+	1.32730i	−1.46051	+	0.931084i	−0.203275	−	0.445110i	−1.12254	−	0.329608i	0.00999087	−	2.73274i	−0.755750	−	0.654861i	−2.35922	−	0.339204i	1.26617	−	2.71971i	1.39502	−	1.20879i
113.14	−0.732726	+	1.14014i	1.28310	+	1.16347i	0.0677890	+	0.148437i	3.54035	+	1.03954i	−2.26668	+	0.610418i	−0.755750	−	0.654861i	−2.90190	−	0.417231i	0.292696	+	2.98569i	−3.77934	+	3.27481i
113.15	−0.645581	+	1.00454i	−0.549837	+	1.64246i	0.238496	+	0.522234i	3.49538	+	1.02634i	−1.29496	−	1.61268i	0.755750	+	0.654861i	−3.04248	−	0.437442i	−2.39536	−	1.80617i	−3.28755	+	2.84868i
113.16	−0.621877	+	0.967660i	−1.59011	−	0.686701i	0.281195	+	0.615732i	0.670051	+	0.196745i	1.65334	−	1.11164i	−0.755750	−	0.654861i	−3.04779	−	0.438206i	2.05688	+	2.18386i	−0.607071	+	0.526030i
113.17	−0.552629	+	0.859908i	1.69926	+	0.335441i	0.396788	+	0.868844i	1.96993	+	0.578425i	−1.22751	+	1.27583i	0.755750	+	0.654861i	−2.98994	−	0.429889i	2.77496	+	1.14000i	−1.58604	+	1.37431i
113.18	−0.542374	+	0.843951i	0.351081	+	1.69610i	0.412747	+	0.903790i	−2.37324	−	0.696847i	−1.62184	−	0.623624i	0.755750	+	0.654861i	−2.97261	−	0.427396i	−2.75348	+	1.19093i	1.87529	−	1.62495i
113.19	−0.497545	+	0.774196i	−0.368438	−	1.69241i	0.479003	+	1.04887i	−0.349963	−	0.102758i	1.49357	+	0.556808i	0.755750	+	0.654861i	−2.87220	−	0.412960i	−2.72851	+	1.24710i	0.253678	−	0.219813i
113.20	−0.437059	+	0.680077i	1.47311	−	0.911006i	0.559346	+	1.22480i	2.18862	+	0.642637i	−0.0242835	+	1.39999i	−0.755750	−	0.654861i	−2.67778	−	0.385007i	1.34013	−	2.68403i	−1.39360	+	1.20756i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
23.d	odd	22	1	inner
69.g	even	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	483.2.u.a	✓	480
3.b	odd	2	1	inner	483.2.u.a	✓	480
23.d	odd	22	1	inner	483.2.u.a	✓	480
69.g	even	22	1	inner	483.2.u.a	✓	480

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
483.2.u.a	✓	480	1.a	even	1	1	trivial
483.2.u.a	✓	480	3.b	odd	2	1	inner
483.2.u.a	✓	480	23.d	odd	22	1	inner
483.2.u.a	✓	480	69.g	even	22	1	inner

Hecke kernels

This newform subspace is the entire newspace $S_{2}^{\mathrm{new}}(483, [\chi])$.