Newform orbit 350.3.v.a

• Label: 350.3.v.a
• Level: $350$
• Weight: $3$
• Character orbit: 350.v
• Analytic conductor: $9.537$
• Analytic rank: $0$
• Dimension: $320$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	350.v (of order \(30\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.53680925261\)
Analytic rank:	\(0\)
Dimension:	\(320\)
Relative dimension:	\(40\) over \(\Q(\zeta_{30})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 320 q - 80 q^{4} + 6 q^{5} + 120 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−0.294032	+	1.38331i	−5.13487	−	2.28619i	−1.82709	−	0.813473i	−0.803113	+	4.93508i	4.67233	−	6.43090i	−6.95693	+	0.775294i	1.66251	−	2.28825i	15.1181	+	16.7903i	−6.59060	−	2.56202i
19.2	−0.294032	+	1.38331i	−4.70789	−	2.09609i	−1.82709	−	0.813473i	−0.569436	−	4.96747i	4.28381	−	5.89616i	4.76630	−	5.12664i	1.66251	−	2.28825i	11.7485	+	13.0480i	7.03898	+	0.672886i
19.3	−0.294032	+	1.38331i	−4.35796	−	1.94029i	−1.82709	−	0.813473i	4.16298	−	2.76941i	3.96540	−	5.45790i	−1.60489	+	6.81354i	1.66251	−	2.28825i	9.20493	+	10.2231i	2.60690	+	6.57298i
19.4	−0.294032	+	1.38331i	−3.59279	−	1.59961i	−1.82709	−	0.813473i	−0.652463	+	4.95725i	3.26915	−	4.49960i	6.94431	−	0.881188i	1.66251	−	2.28825i	4.32719	+	4.80584i	−6.66556	−	2.36015i
19.5	−0.294032	+	1.38331i	−2.82522	−	1.25787i	−1.82709	−	0.813473i	−4.99949	−	0.0713720i	2.57073	−	3.53830i	−4.13629	−	5.64722i	1.66251	−	2.28825i	0.377457	+	0.419209i	1.56874	−	6.89486i
19.6	−0.294032	+	1.38331i	−2.55587	−	1.13794i	−1.82709	−	0.813473i	−2.92322	−	4.05645i	2.32564	−	3.20096i	−5.16714	+	4.72236i	1.66251	−	2.28825i	−0.784643	−	0.871434i	6.47085	−	2.85099i
19.7	−0.294032	+	1.38331i	−2.53211	−	1.12737i	−1.82709	−	0.813473i	2.93526	+	4.04774i	2.30402	−	3.17121i	2.47368	+	6.54835i	1.66251	−	2.28825i	−0.881565	−	0.979077i	−6.46234	+	2.87021i
19.8	−0.294032	+	1.38331i	−1.61896	−	0.720807i	−1.82709	−	0.813473i	3.91600	−	3.10885i	1.47312	−	2.02758i	−4.12272	−	5.65714i	1.66251	−	2.28825i	−3.92071	−	4.35439i	3.14907	+	6.33114i
19.9	−0.294032	+	1.38331i	−1.25896	−	0.560523i	−1.82709	−	0.813473i	4.88180	+	1.08075i	1.14555	−	1.57671i	5.53021	−	4.29147i	1.66251	−	2.28825i	−4.75139	−	5.27696i	−2.93041	+	6.43527i
19.10	−0.294032	+	1.38331i	−0.0741053	−	0.0329938i	−1.82709	−	0.813473i	1.15758	+	4.86416i	0.0674299	−	0.0928093i	−5.84333	−	3.85428i	1.66251	−	2.28825i	−6.01777	−	6.68341i	−7.06900	+	0.171077i
19.11	−0.294032	+	1.38331i	0.968136	+	0.431042i	−1.82709	−	0.813473i	−2.99339	−	4.00495i	−0.880927	+	1.21249i	5.77801	+	3.95153i	1.66251	−	2.28825i	−5.27068	−	5.85369i	6.42023	−	2.96321i
19.12	−0.294032	+	1.38331i	0.986823	+	0.439362i	−1.82709	−	0.813473i	3.46365	−	3.60599i	−0.897931	+	1.23590i	4.92842	+	4.97098i	1.66251	−	2.28825i	−5.24139	−	5.82116i	3.96977	+	5.85157i
19.13	−0.294032	+	1.38331i	1.60887	+	0.716316i	−1.82709	−	0.813473i	−4.32408	+	2.51045i	−1.46395	+	2.01495i	−3.94060	+	5.78547i	1.66251	−	2.28825i	−3.94682	−	4.38338i	−2.20131	−	6.71969i
19.14	−0.294032	+	1.38331i	2.17642	+	0.969004i	−1.82709	−	0.813473i	−1.12859	+	4.87096i	−1.98037	+	2.72574i	5.05324	−	4.84405i	1.66251	−	2.28825i	−2.22434	−	2.47039i	−6.40621	−	2.99341i
19.15	−0.294032	+	1.38331i	2.37320	+	1.05662i	−1.82709	−	0.813473i	−4.99168	+	0.288313i	−2.15943	+	2.97220i	5.65904	−	4.12011i	1.66251	−	2.28825i	−1.50652	−	1.67316i	1.06889	−	6.98981i
19.16	−0.294032	+	1.38331i	3.00253	+	1.33681i	−1.82709	−	0.813473i	4.68905	+	1.73574i	−2.73207	+	3.76037i	−5.54036	+	4.27836i	1.66251	−	2.28825i	1.20596	+	1.33936i	−3.77979	+	5.97605i
19.17	−0.294032	+	1.38331i	3.04935	+	1.35766i	−1.82709	−	0.813473i	−1.88763	−	4.62999i	−2.77467	+	3.81901i	−3.22746	−	6.21156i	1.66251	−	2.28825i	1.43315	+	1.59167i	6.95974	−	1.24982i
19.18	−0.294032	+	1.38331i	4.25827	+	1.89590i	−1.82709	−	0.813473i	4.98451	−	0.393315i	−3.87468	+	5.33304i	1.11259	−	6.91102i	1.66251	−	2.28825i	8.51620	+	9.45820i	−0.921525	+	7.01076i
19.19	−0.294032	+	1.38331i	5.03638	+	2.24234i	−1.82709	−	0.813473i	0.927628	+	4.91320i	−4.58270	+	6.30755i	5.46120	+	4.37895i	1.66251	−	2.28825i	14.3148	+	15.8982i	−7.06922	−	0.161439i
19.20	−0.294032	+	1.38331i	5.19874	+	2.31463i	−1.82709	−	0.813473i	−2.34060	−	4.41832i	−4.73044	+	6.51090i	−0.189291	+	6.99744i	1.66251	−	2.28825i	15.6473	+	17.3780i	6.80012	−	1.93865i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.d	odd	6	1	inner
25.e	even	10	1	inner
175.u	odd	30	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	350.3.v.a	✓	320
7.d	odd	6	1	inner	350.3.v.a	✓	320
25.e	even	10	1	inner	350.3.v.a	✓	320
175.u	odd	30	1	inner	350.3.v.a	✓	320

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
350.3.v.a	✓	320	1.a	even	1	1	trivial
350.3.v.a	✓	320	7.d	odd	6	1	inner
350.3.v.a	✓	320	25.e	even	10	1	inner
350.3.v.a	✓	320	175.u	odd	30	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(350, [\chi])\).