Newform orbit 429.2.bv.a

• Label: 429.2.bv.a
• Level: $429$
• Weight: $2$
• Character orbit: 429.bv
• Analytic conductor: $3.426$
• Analytic rank: $0$
• Dimension: $832$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bv (of order \(60\), degree \(16\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.42558224671\)
Analytic rank:	\(0\)
Dimension:	\(832\)
Relative dimension:	\(52\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
20.1	−2.76683	−	0.145003i	1.66622	+	0.472982i	5.64525	+	0.593340i	−0.523203	−	0.266585i	−4.54156	−	1.55027i	0.0260847	+	0.0322120i	−10.0604	−	1.59341i	2.55258	+	1.57618i	1.40895	+	0.813460i
20.2	−2.62774	−	0.137714i	−0.224523	+	1.71744i	4.89702	+	0.514697i	1.89968	+	0.967935i	0.826504	−	4.48206i	−0.815502	−	1.00706i	−7.59931	−	1.20361i	−2.89918	−	0.771208i	−4.85857	−	2.80510i
20.3	−2.50925	−	0.131504i	0.691538	−	1.58801i	4.29002	+	0.450899i	−2.60114	−	1.32535i	−1.94407	+	3.89378i	−2.59163	−	3.20040i	−5.74193	−	0.909433i	−2.04355	−	2.19634i	6.35263	+	3.66769i
20.4	−2.37518	−	0.124478i	−1.72714	−	0.130360i	3.63696	+	0.382260i	1.22228	+	0.622785i	4.08604	+	0.524621i	−1.12395	−	1.38796i	−3.89254	−	0.616518i	2.96601	+	0.450301i	−2.82563	−	1.63138i
20.5	−2.28988	−	0.120007i	1.09330	−	1.34339i	3.24009	+	0.340548i	3.86458	+	1.96910i	−2.66474	+	2.94499i	−1.55450	−	1.91965i	−2.84897	−	0.451233i	−0.609383	−	2.93746i	−8.61310	−	4.97278i
20.6	−2.28609	−	0.119809i	−0.750909	−	1.56081i	3.22281	+	0.338731i	0.125105	+	0.0637444i	1.52965	+	3.65812i	0.00715252	+	0.00883262i	−2.80496	−	0.444262i	−1.87227	+	2.34406i	−0.278365	−	0.160714i
20.7	−2.16363	−	0.113391i	−1.53088	+	0.810191i	2.67939	+	0.281615i	2.44832	+	1.24748i	3.40412	−	1.57936i	2.26128	+	2.79244i	−1.48541	−	0.235267i	1.68718	−	2.48061i	−5.15579	−	2.97670i
20.8	−2.15849	−	0.113122i	1.68832	−	0.386733i	2.65724	+	0.279288i	0.408417	+	0.208099i	−3.68798	+	0.643774i	2.50194	+	3.08964i	−1.43436	−	0.227180i	2.70088	−	1.30586i	−0.858025	−	0.495381i
20.9	−2.11349	−	0.110763i	−0.0744693	+	1.73045i	2.46552	+	0.259137i	−1.61438	−	0.822569i	0.349060	−	3.64904i	0.621753	+	0.767801i	−1.00148	−	0.158619i	−2.98891	−	0.257731i	3.32087	+	1.91730i
20.10	−1.99540	−	0.104575i	1.06644	+	1.36481i	1.98165	+	0.208280i	−2.39161	−	1.21859i	−1.98525	−	2.83487i	−0.280750	−	0.346697i	0.0146712	+	0.00232369i	−0.725421	+	2.91097i	4.64480	+	2.68168i
20.11	−1.79980	−	0.0943236i	−1.44075	−	0.961374i	1.24134	+	0.130471i	−2.65618	−	1.35339i	2.50238	+	1.86618i	1.02884	+	1.27051i	1.33830	+	0.211966i	1.15152	+	2.77020i	4.65295	+	2.68638i
20.12	−1.53416	−	0.0804022i	1.22300	+	1.22648i	0.358152	+	0.0376433i	3.02311	+	1.54035i	−1.77768	−	1.97996i	2.44154	+	3.01505i	2.48827	+	0.394104i	−0.00852784	+	2.99999i	−4.51410	−	2.60622i
20.13	−1.49304	−	0.0782468i	−1.51095	+	0.846781i	0.233997	+	0.0245940i	−2.86498	−	1.45978i	2.32216	−	1.14605i	−1.76998	−	2.18574i	2.60592	+	0.412737i	1.56592	−	2.55888i	4.16330	+	2.40368i
20.14	−1.40019	−	0.0733811i	−0.460922	−	1.66960i	−0.0338826	−	0.00356121i	2.36606	+	1.20557i	0.522864	+	2.37158i	0.593855	+	0.733350i	2.81689	+	0.446151i	−2.57510	+	1.53911i	−3.22448	−	1.86166i
20.15	−1.36547	−	0.0715611i	0.862643	+	1.50195i	−0.129662	−	0.0136280i	1.20967	+	0.616356i	−1.07043	−	2.11259i	−2.59780	−	3.20801i	2.87709	+	0.455686i	−1.51169	+	2.59129i	−1.60765	−	0.928179i
20.16	−1.33300	−	0.0698593i	1.66414	−	0.480245i	−0.217048	−	0.0228127i	−0.706650	−	0.360056i	−2.25184	+	0.523909i	−1.22329	−	1.51064i	2.92451	+	0.463197i	2.53873	−	1.59839i	0.916807	+	0.529319i
20.17	−1.20280	−	0.0630360i	−1.28110	+	1.16567i	−0.546295	−	0.0574179i	−0.505038	−	0.257330i	1.61438	−	1.32131i	1.25810	+	1.55363i	3.03270	+	0.480333i	0.282417	−	2.98668i	0.591237	+	0.341351i
20.18	−1.03397	−	0.0541882i	1.05441	−	1.37413i	−0.922880	−	0.0969986i	0.459701	+	0.234229i	−1.16469	+	1.36367i	−0.356420	−	0.440142i	2.99427	+	0.474245i	−0.776456	−	2.89778i	−0.462625	−	0.267097i
20.19	−1.03370	−	0.0541738i	−1.71154	−	0.265772i	−0.923448	−	0.0970583i	2.13376	+	1.08720i	1.75482	+	0.367448i	−2.13395	−	2.63521i	2.99405	+	0.474211i	2.85873	+	0.909757i	−2.14676	−	1.23943i
20.20	−0.719787	−	0.0377225i	−0.704391	−	1.58235i	−1.47237	−	0.154753i	−2.50517	−	1.27645i	0.447321	+	1.16553i	−3.13449	−	3.87078i	2.47776	+	0.392439i	−2.00767	+	2.22919i	1.75504	+	1.01327i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
11.c	even	5	1	inner
13.f	odd	12	1	inner
33.h	odd	10	1	inner
39.k	even	12	1	inner
143.x	odd	60	1	inner
429.bv	even	60	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	429.2.bv.a	✓	832
3.b	odd	2	1	inner	429.2.bv.a	✓	832
11.c	even	5	1	inner	429.2.bv.a	✓	832
13.f	odd	12	1	inner	429.2.bv.a	✓	832
33.h	odd	10	1	inner	429.2.bv.a	✓	832
39.k	even	12	1	inner	429.2.bv.a	✓	832
143.x	odd	60	1	inner	429.2.bv.a	✓	832
429.bv	even	60	1	inner	429.2.bv.a	✓	832

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
429.2.bv.a	✓	832	1.a	even	1	1	trivial
429.2.bv.a	✓	832	3.b	odd	2	1	inner
429.2.bv.a	✓	832	11.c	even	5	1	inner
429.2.bv.a	✓	832	13.f	odd	12	1	inner
429.2.bv.a	✓	832	33.h	odd	10	1	inner
429.2.bv.a	✓	832	39.k	even	12	1	inner
429.2.bv.a	✓	832	143.x	odd	60	1	inner
429.2.bv.a	✓	832	429.bv	even	60	1	inner

Hecke kernels

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