Newform orbit 429.2.be.a

• Label: 429.2.be.a
• Level: $429$
• Weight: $2$
• Character orbit: 429.be
• Analytic conductor: $3.426$
• Analytic rank: $0$
• Dimension: $184$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.be (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.42558224671\)
Analytic rank:	\(0\)
Dimension:	\(184\)
Relative dimension:	\(46\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 184 q - 12 q^{6} + 12 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
89.1	−2.56597	−	0.687549i	0.227829	−	1.71700i	4.37942	+	2.52846i	2.70172	−	2.70172i	−1.76513	+	4.24913i	0.243586	+	0.909075i	−5.74218	−	5.74218i	−2.89619	−	0.782365i	−8.79010	+	5.07497i
89.2	−2.48352	−	0.665458i	−1.51130	−	0.846155i	3.99300	+	2.30536i	−0.0572884	+	0.0572884i	3.19026	+	3.10715i	−0.793036	−	2.95965i	−4.74647	−	4.74647i	1.56804	+	2.55758i	0.180400	−	0.104154i
89.3	−2.44763	−	0.655840i	1.31899	−	1.12261i	3.82870	+	2.21050i	−1.62249	+	1.62249i	−3.96466	+	1.88269i	0.335823	+	1.25331i	−4.33792	−	4.33792i	0.479486	−	2.96143i	5.03534	−	2.90715i
89.4	−2.43755	−	0.653139i	0.235409	+	1.71598i	3.78299	+	2.18411i	1.30401	−	1.30401i	0.546952	−	4.33653i	−1.18861	−	4.43596i	−4.22588	−	4.22588i	−2.88917	+	0.807913i	−4.03028	+	2.32688i
89.5	−2.39352	−	0.641342i	1.64395	+	0.545381i	3.58556	+	2.07013i	−0.0323011	+	0.0323011i	−3.58504	−	2.35971i	0.0457503	+	0.170743i	−3.75010	−	3.75010i	2.40512	+	1.79315i	0.0980293	−	0.0565972i
89.6	−2.25191	−	0.603398i	−1.65469	+	0.511873i	2.97497	+	1.71760i	2.28764	−	2.28764i	4.03507	−	0.154258i	0.850397	+	3.17372i	−2.36594	−	2.36594i	2.47597	−	1.69398i	−6.53192	+	3.77121i
89.7	−2.20878	−	0.591842i	−1.22709	−	1.22240i	2.79640	+	1.61450i	−2.05423	+	2.05423i	1.98690	+	3.42626i	0.902198	+	3.36705i	−1.98722	−	1.98722i	0.0114791	+	2.99998i	5.75313	−	3.32157i
89.8	−1.99225	−	0.533822i	−1.33180	+	1.10738i	1.95204	+	1.12701i	−0.191278	+	0.191278i	3.24443	−	1.49524i	−0.125579	−	0.468666i	−0.370477	−	0.370477i	0.547407	−	2.94963i	0.483182	−	0.278965i
89.9	−1.76077	−	0.471796i	1.54331	+	0.786256i	1.14566	+	0.661445i	1.75250	−	1.75250i	−2.34645	−	2.11254i	0.531771	+	1.98460i	0.872774	+	0.872774i	1.76360	+	2.42687i	−3.91258	+	2.25893i
89.10	−1.72773	−	0.462944i	0.702909	+	1.58301i	1.03868	+	0.599682i	−2.41452	+	2.41452i	−0.481591	−	3.06042i	−0.301061	−	1.12357i	1.01263	+	1.01263i	−2.01184	+	2.22542i	5.28942	−	3.05385i
89.11	−1.52845	−	0.409546i	−0.446060	−	1.67363i	0.436367	+	0.251936i	−0.731227	+	0.731227i	−0.00364908	+	2.74073i	−0.466780	−	1.74204i	1.67402	+	1.67402i	−2.60206	+	1.49308i	1.41711	−	0.818170i
89.12	−1.52005	−	0.407295i	1.56613	−	0.739746i	0.412602	+	0.238216i	1.90285	−	1.90285i	−2.68189	+	0.486569i	−1.32203	−	4.93388i	1.69535	+	1.69535i	1.90555	−	2.31708i	−3.66744	+	2.11740i
89.13	−1.50551	−	0.403401i	0.00525696	+	1.73204i	0.371782	+	0.214648i	−0.722785	+	0.722785i	0.690793	−	2.60973i	1.16889	+	4.36236i	1.73109	+	1.73109i	−2.99994	+	0.0182105i	1.37973	−	0.796589i
89.14	−1.32901	−	0.356107i	1.71883	−	0.213571i	−0.0925961	−	0.0534604i	−2.48553	+	2.48553i	−2.36040	−	0.328250i	−0.825366	−	3.08031i	2.04983	+	2.04983i	2.90877	−	0.734187i	4.18841	−	2.41818i
89.15	−1.22945	−	0.329429i	−1.72326	−	0.174256i	−0.329037	−	0.189970i	0.992009	−	0.992009i	2.06125	+	0.781932i	−0.778711	−	2.90619i	2.14199	+	2.14199i	2.93927	+	0.600579i	−1.54642	+	0.892825i
89.16	−0.954637	−	0.255794i	1.35903	−	1.07380i	−0.886149	−	0.511619i	−1.59904	+	1.59904i	−1.57205	+	0.677454i	0.743538	+	2.77492i	2.11277	+	2.11277i	0.693924	−	2.91864i	1.93553	−	1.11748i
89.17	−0.810471	−	0.217165i	−1.43084	−	0.976061i	−1.12235	−	0.647988i	1.96327	−	1.96327i	0.947689	+	1.10180i	1.13192	+	4.22438i	1.95552	+	1.95552i	1.09461	+	2.79318i	−2.01753	+	1.16482i
89.18	−0.781729	−	0.209464i	0.746974	+	1.56270i	−1.16483	−	0.672513i	2.62100	−	2.62100i	−0.256602	−	1.37807i	0.0507104	+	0.189254i	1.91424	+	1.91424i	−1.88406	+	2.33459i	−2.59791	+	1.49990i
89.19	−0.745893	−	0.199861i	−0.815569	+	1.52802i	−1.21564	−	0.701849i	−0.458199	+	0.458199i	0.913720	−	0.976739i	−0.672164	−	2.50855i	1.85853	+	1.85853i	−1.66969	−	2.49241i	0.433344	−	0.250191i
89.20	−0.283022	−	0.0758356i	−1.01211	−	1.40557i	−1.65770	−	0.957074i	−2.69708	+	2.69708i	0.179857	+	0.474562i	−0.867145	−	3.23623i	0.810959	+	0.810959i	−0.951270	+	2.84519i	0.967866	−	0.558798i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
13.f	odd	12	1	inner
39.k	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	429.2.be.a	✓	184
3.b	odd	2	1	inner	429.2.be.a	✓	184
13.f	odd	12	1	inner	429.2.be.a	✓	184
39.k	even	12	1	inner	429.2.be.a	✓	184

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
429.2.be.a	✓	184	1.a	even	1	1	trivial
429.2.be.a	✓	184	3.b	odd	2	1	inner
429.2.be.a	✓	184	13.f	odd	12	1	inner
429.2.be.a	✓	184	39.k	even	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(429, [\chi])\).