Newform orbit 201.2.j.a

• Label: 201.2.j.a
• Level: $201$
• Weight: $2$
• Character orbit: 201.j
• Analytic conductor: $1.605$
• Analytic rank: $0$
• Dimension: $200$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.j (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.60499308063\)
Analytic rank:	\(0\)
Dimension:	\(200\)
Relative dimension:	\(20\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 200 q - 11 q^{3} - 34 q^{4} - 7 q^{6} - 22 q^{7} + 3 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1	−1.80413	+	2.08208i	−1.15463	−	1.29106i	−0.795528	−	5.53302i	−0.470328	+	0.138101i	4.77118	−	0.0747868i	−0.367215	−	0.318193i	8.32012	+	5.34702i	−0.333667	+	2.98139i	0.560996	−	1.22841i
5.2	−1.48703	+	1.71613i	−0.582539	+	1.63115i	−0.449198	−	3.12424i	1.31922	−	0.387358i	−1.93301	−	3.42529i	−3.29666	−	2.85657i	2.20900	+	1.41964i	−2.32130	−	1.90042i	−1.29697	+	2.83997i
5.3	−1.45043	+	1.67388i	1.46447	+	0.924840i	−0.413514	−	2.87605i	1.41694	−	0.416050i	−3.67218	+	1.10994i	1.28570	+	1.11407i	1.68743	+	1.08444i	1.28934	+	2.70880i	−1.35875	+	2.97524i
5.4	−1.36124	+	1.57095i	0.885763	−	1.48843i	−0.330294	−	2.29725i	1.00399	−	0.294799i	1.13252	+	3.41760i	−0.415510	−	0.360042i	0.561099	+	0.360596i	−1.43085	−	2.63679i	−0.903560	+	1.97852i
5.5	−1.16364	+	1.34291i	−1.67608	+	0.436744i	−0.164727	−	1.14570i	−2.73659	+	0.803536i	1.36385	−	2.75905i	0.246444	+	0.213545i	−1.25944	−	0.809393i	2.61851	−	1.46404i	2.10533	−	4.61004i
5.6	−0.706711	+	0.815588i	−1.69171	−	0.371647i	0.118886	+	0.826873i	3.89728	−	1.14434i	1.49866	−	1.11709i	−1.64135	−	1.42224i	−2.57413	−	1.65429i	2.72376	+	1.25744i	−1.82094	+	3.98729i
5.7	−0.634589	+	0.732355i	1.17689	+	1.27080i	0.150989	+	1.05015i	−2.77562	+	0.814995i	−1.67752	+	0.0554604i	0.0640238	+	0.0554769i	−2.49533	−	1.60365i	−0.229880	+	2.99118i	1.16451	−	2.54992i
5.8	−0.422797	+	0.487934i	−0.589489	+	1.62865i	0.225308	+	1.56705i	1.17382	−	0.344663i	−0.545439	−	0.976220i	2.44605	+	2.11952i	−1.94615	−	1.25071i	−2.30500	−	1.92014i	−0.328113	+	0.718466i
5.9	−0.401105	+	0.462899i	−0.467910	−	1.66765i	0.231239	+	1.60830i	−2.18653	+	0.642023i	0.959636	+	0.452308i	−3.07269	−	2.66251i	−1.86777	−	1.20035i	−2.56212	+	1.56062i	0.579835	−	1.26966i
5.10	−0.333078	+	0.384392i	1.47238	−	0.912186i	0.247813	+	1.72358i	2.02247	−	0.593851i	−0.139781	+	0.869802i	0.616666	+	0.534344i	−1.60083	−	1.02879i	1.33583	−	2.68618i	−0.445368	+	0.975220i
5.11	0.333078	−	0.384392i	1.65359	−	0.515399i	0.247813	+	1.72358i	−2.02247	+	0.593851i	0.352659	−	0.807295i	0.616666	+	0.534344i	1.60083	+	1.02879i	2.46873	−	1.70452i	−0.445368	+	0.975220i
5.12	0.401105	−	0.462899i	0.953911	+	1.44570i	0.231239	+	1.60830i	2.18653	−	0.642023i	1.05183	+	0.138313i	−3.07269	−	2.66251i	1.86777	+	1.20035i	−1.18011	+	2.75814i	0.579835	−	1.26966i
5.13	0.422797	−	0.487934i	−1.61689	−	0.621033i	0.225308	+	1.56705i	−1.17382	+	0.344663i	−0.986637	+	0.526362i	2.44605	+	2.11952i	1.94615	+	1.25071i	2.22864	+	2.00828i	−0.328113	+	0.718466i
5.14	0.634589	−	0.732355i	−0.189712	−	1.72163i	0.150989	+	1.05015i	2.77562	−	0.814995i	−1.38123	−	0.953590i	0.0640238	+	0.0554769i	2.49533	+	1.60365i	−2.92802	+	0.653229i	1.16451	−	2.54992i
5.15	0.706711	−	0.815588i	−0.826962	+	1.52189i	0.118886	+	0.826873i	−3.89728	+	1.14434i	0.656808	+	1.74999i	−1.64135	−	1.42224i	2.57413	+	1.65429i	−1.63227	−	2.51708i	−1.82094	+	3.98729i
5.16	1.16364	−	1.34291i	−1.42767	+	0.980693i	−0.164727	−	1.14570i	2.73659	−	0.803536i	−0.344310	+	3.05841i	0.246444	+	0.213545i	1.25944	+	0.809393i	1.07648	−	2.80021i	2.10533	−	4.61004i
5.17	1.36124	−	1.57095i	1.70493	+	0.305299i	−0.330294	−	2.29725i	−1.00399	+	0.294799i	2.80043	−	2.26278i	−0.415510	−	0.360042i	−0.561099	−	0.360596i	2.81358	+	1.04103i	−0.903560	+	1.97852i
5.18	1.45043	−	1.67388i	0.260076	−	1.71241i	−0.413514	−	2.87605i	−1.41694	+	0.416050i	−2.48916	−	2.91907i	1.28570	+	1.11407i	−1.68743	−	1.08444i	−2.86472	−	0.890717i	−1.35875	+	2.97524i
5.19	1.48703	−	1.71613i	−1.61422	−	0.627922i	−0.449198	−	3.12424i	−1.31922	+	0.387358i	−3.47800	+	1.83647i	−3.29666	−	2.85657i	−2.20900	−	1.41964i	2.21143	+	2.02721i	−1.29697	+	2.83997i
5.20	1.80413	−	2.08208i	0.219597	+	1.71807i	−0.795528	−	5.53302i	0.470328	−	0.138101i	3.97334	+	2.64241i	−0.367215	−	0.318193i	−8.32012	−	5.34702i	−2.90355	+	0.754566i	0.560996	−	1.22841i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
67.f	odd	22	1	inner
201.j	even	22	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	201.2.j.a	✓	200
3.b	odd	2	1	inner	201.2.j.a	✓	200
67.f	odd	22	1	inner	201.2.j.a	✓	200
201.j	even	22	1	inner	201.2.j.a	✓	200

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
201.2.j.a	✓	200	1.a	even	1	1	trivial
201.2.j.a	✓	200	3.b	odd	2	1	inner
201.2.j.a	✓	200	67.f	odd	22	1	inner
201.2.j.a	✓	200	201.j	even	22	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(201, [\chi])\).