Newform orbit 429.2.j.a

• Label: 429.2.j.a
• Level: $429$
• Weight: $2$
• Character orbit: 429.j
• Analytic conductor: $3.426$
• Analytic rank: $0$
• Dimension: $96$
• CM: no
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(3.42558224671\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(48\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
122.1	−1.95700	−	1.95700i	1.66851	+	0.464826i			5.65973i	−0.288277	−	0.288277i	−2.35562	−	4.17495i	−2.20581	−	2.20581i	7.16211	−	7.16211i	2.56787	+	1.55114i			1.12832i
122.2	−1.89533	−	1.89533i	−0.602141	+	1.62402i			5.18453i	1.30667	+	1.30667i	4.21929	−	1.93679i	3.41860	+	3.41860i	6.03572	−	6.03572i	−2.27485	−	1.95577i		−	4.95311i
122.3	−1.84950	−	1.84950i	−1.73089	−	0.0633404i			4.84133i	2.48780	+	2.48780i	3.08414	+	3.31844i	−2.91775	−	2.91775i	5.25505	−	5.25505i	2.99198	+	0.219271i		−	9.20239i
122.4	−1.78236	−	1.78236i	−1.03830	+	1.38634i			4.35365i	−3.07379	−	3.07379i	4.32159	−	0.620342i	−1.36462	−	1.36462i	4.19506	−	4.19506i	−0.843882	−	2.87887i			10.9572i
122.5	−1.74176	−	1.74176i	−0.954649	−	1.44521i			4.06743i	−0.190803	−	0.190803i	−0.854447	+	4.17998i	1.94400	+	1.94400i	3.60095	−	3.60095i	−1.17729	+	2.75934i			0.664665i
122.6	−1.70776	−	1.70776i	0.636556	−	1.61084i			3.83287i	0.490801	+	0.490801i	−3.83800	+	1.66383i	−0.206749	−	0.206749i	3.13009	−	3.13009i	−2.18959	−	2.05078i		−	1.67634i
122.7	−1.52670	−	1.52670i	1.68807	−	0.387848i			2.66165i	1.02510	+	1.02510i	−3.16931	−	1.98505i	0.667364	+	0.667364i	1.01014	−	1.01014i	2.69915	−	1.30943i		−	3.13005i
122.8	−1.43577	−	1.43577i	−1.73083	−	0.0650121i			2.12285i	−1.59194	−	1.59194i	2.39173	+	2.57841i	1.33791	+	1.33791i	0.176380	−	0.176380i	2.99155	+	0.225050i			4.57130i
122.9	−1.43233	−	1.43233i	0.643764	−	1.60797i			2.10314i	−2.03215	−	2.03215i	−3.22523	+	1.38106i	−3.19246	−	3.19246i	0.147729	−	0.147729i	−2.17114	−	2.07031i			5.82141i
122.10	−1.37738	−	1.37738i	1.00936	+	1.40755i			1.79436i	2.82918	+	2.82918i	0.548456	−	3.32900i	−0.289134	−	0.289134i	−0.283251	+	0.283251i	−0.962383	+	2.84145i		−	7.79370i
122.11	−1.28581	−	1.28581i	0.911426	+	1.47286i			1.30661i	−1.56311	−	1.56311i	0.721891	−	3.06573i	−0.788371	−	0.788371i	−0.891573	+	0.891573i	−1.33861	+	2.68480i			4.01973i
122.12	−1.28495	−	1.28495i	−0.594101	+	1.62697i			1.30220i	0.959579	+	0.959579i	2.85397	−	1.32719i	−1.57675	−	1.57675i	−0.896640	+	0.896640i	−2.29409	−	1.93317i		−	2.46603i
122.13	−1.16086	−	1.16086i	−1.66333	+	0.483035i			0.695179i	0.163665	+	0.163665i	2.49163	+	1.37016i	0.204315	+	0.204315i	−1.51471	+	1.51471i	2.53335	−	1.60690i		−	0.379984i
122.14	−0.972463	−	0.972463i	1.43733	−	0.966479i		−	0.108632i	1.52250	+	1.52250i	−2.33762	−	0.457885i	2.37496	+	2.37496i	−2.05057	+	2.05057i	1.13184	−	2.77830i		−	2.96115i
122.15	−0.943039	−	0.943039i	−1.40657	−	1.01073i		−	0.221356i	−0.0801747	−	0.0801747i	0.373288	+	2.27960i	−3.37063	−	3.37063i	−2.09482	+	2.09482i	0.956852	+	2.84331i			0.151216i
122.16	−0.786557	−	0.786557i	−0.138475	−	1.72651i		−	0.762656i	−2.59877	−	2.59877i	−1.24908	+	1.46691i	1.66123	+	1.66123i	−2.17299	+	2.17299i	−2.96165	+	0.478155i			4.08816i
122.17	−0.727121	−	0.727121i	1.73181	+	0.0289503i		−	0.942589i	−1.91531	−	1.91531i	−1.23818	−	1.28029i	−1.22176	−	1.22176i	−2.13962	+	2.13962i	2.99832	+	0.100273i			2.78533i
122.18	−0.680371	−	0.680371i	−0.131936	+	1.72702i		−	1.07419i	−1.70906	−	1.70906i	1.26478	−	1.08525i	2.81165	+	2.81165i	−2.09159	+	2.09159i	−2.96519	−	0.455712i			2.32560i
122.19	−0.487825	−	0.487825i	0.738212	−	1.56686i		−	1.52405i	2.39011	+	2.39011i	−1.12447	+	0.404234i	−2.10889	−	2.10889i	−1.71912	+	1.71912i	−1.91009	−	2.31335i		−	2.33191i
122.20	−0.388797	−	0.388797i	1.29884	+	1.14586i		−	1.69767i	1.22711	+	1.22711i	−0.0594784	−	0.950496i	3.02639	+	3.02639i	−1.43765	+	1.43765i	0.373993	+	2.97660i		−	0.954196i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
13.d	odd	4	1	inner
39.f	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	429.2.j.a	✓	96
3.b	odd	2	1	inner	429.2.j.a	✓	96
13.d	odd	4	1	inner	429.2.j.a	✓	96
39.f	even	4	1	inner	429.2.j.a	✓	96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
429.2.j.a	✓	96	1.a	even	1	1	trivial
429.2.j.a	✓	96	3.b	odd	2	1	inner
429.2.j.a	✓	96	13.d	odd	4	1	inner
429.2.j.a	✓	96	39.f	even	4	1	inner

Hecke kernels

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