Newform orbit 405.3.v.a

• Label: 405.3.v.a
• Level: $405$
• Weight: $3$
• Character orbit: 405.v
• Analytic conductor: $11.035$
• Analytic rank: $0$
• Dimension: $1908$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.v (of order \(54\), degree \(18\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.0354507066\)
Analytic rank:	\(0\)
Dimension:	\(1908\)
Relative dimension:	\(106\) over \(\Q(\zeta_{54})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1908 q - 36 q^{4} - 18 q^{5} - 36 q^{6} - 36 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
14.1	−3.29799	+	2.16912i	2.05833	+	2.18250i	4.58734	−	10.6346i	2.64539	+	4.24287i	−11.5224	−	2.73310i	−0.595301	+	5.09312i	5.19702	+	29.4738i	−0.526593	+	8.98458i	−17.9278	−	8.25477i
14.2	−3.29100	+	2.16452i	0.378431	−	2.97604i	4.56118	−	10.5740i	1.00021	−	4.89894i	5.19628	+	10.6132i	−1.20936	+	10.3468i	5.14083	+	29.1551i	−8.71358	−	2.25245i	7.31217	+	18.2874i
14.3	−3.11612	+	2.04950i	−0.0376677	+	2.99976i	3.92541	−	9.10012i	−4.39018	−	2.39297i	−6.03065	−	9.42482i	0.755623	−	6.46477i	3.82807	+	21.7101i	−8.99716	−	0.225988i	18.5847	−	1.54089i
14.4	−3.10535	+	2.04242i	−1.80542	−	2.39593i	3.88738	−	9.01197i	−4.66601	+	1.79675i	10.4999	+	3.75276i	0.313964	−	2.68613i	3.75287	+	21.2836i	−2.48093	+	8.65130i	10.8199	−	15.1095i
14.5	−3.09798	+	2.03757i	−2.96105	−	0.481829i	3.86144	−	8.95182i	4.99847	−	0.123857i	10.1550	−	4.54066i	0.0193658	−	0.165685i	3.70179	+	20.9939i	8.53568	+	2.85344i	−15.2328	+	10.5684i
14.6	−3.03761	+	1.99787i	2.82548	−	1.00831i	3.65129	−	8.46463i	−4.45097	+	2.27791i	−6.56823	+	8.70778i	0.0327536	−	0.280225i	3.29468	+	18.6851i	6.96663	−	5.69790i	8.96934	−	15.8119i
14.7	−3.02065	+	1.98671i	−2.13396	+	2.10860i	3.59297	−	8.32944i	−0.293924	+	4.99135i	2.25677	−	10.6089i	1.40605	−	12.0295i	3.18385	+	18.0565i	0.107596	−	8.99936i	−9.02854	−	15.6611i
14.8	−2.91878	+	1.91971i	2.16002	+	2.08190i	3.24967	−	7.53358i	2.77905	−	4.15655i	−10.3013	−	1.93001i	0.955303	−	8.17314i	2.55067	+	14.4656i	0.331344	+	8.99390i	−0.132064	+	17.4670i
14.9	−2.88393	+	1.89679i	2.57449	−	1.54013i	3.13491	−	7.26753i	0.0482909	−	4.99977i	−4.50334	+	9.32488i	1.25631	−	10.7484i	2.34654	+	13.3079i	4.25601	−	7.93010i	9.34423	+	14.5106i
14.10	−2.88369	+	1.89664i	0.354778	−	2.97895i	3.13415	−	7.26576i	2.30306	+	4.43801i	4.62691	+	9.26326i	1.14367	−	9.78476i	2.34520	+	13.3003i	−8.74827	−	2.11373i	−15.0586	−	8.42978i
14.11	−2.88281	+	1.89606i	−1.00002	+	2.82842i	3.13127	−	7.25910i	2.15960	−	4.50956i	−2.47998	−	10.0499i	−0.737294	+	6.30795i	2.34013	+	13.2716i	−6.99992	−	5.65695i	2.32465	+	17.0950i
14.12	−2.79121	+	1.83581i	−2.95352	+	0.526044i	2.83633	−	6.57536i	−3.56714	−	3.50365i	7.27817	−	6.89038i	−0.206579	+	1.76739i	1.83379	+	10.3999i	8.44656	−	3.10736i	16.3886	+	3.23083i
14.13	−2.56750	+	1.68867i	2.91286	+	0.717816i	2.15613	−	4.99846i	−3.19261	−	3.84802i	−8.69092	+	3.07587i	−1.30556	+	11.1697i	0.770386	+	4.36908i	7.96948	+	4.18179i	14.6951	+	4.48851i
14.14	−2.55778	+	1.68228i	−2.46744	−	1.70638i	2.12786	−	4.93293i	−1.25774	+	4.83922i	9.18178	+	0.213634i	−1.10795	+	9.47914i	0.729525	+	4.13734i	3.17651	+	8.42079i	−4.92390	−	14.4935i
14.15	−2.55488	+	1.68037i	−1.51015	+	2.59219i	2.11945	−	4.91343i	4.24733	+	2.63822i	−0.497587	−	9.16035i	−0.921005	+	7.87971i	0.717422	+	4.06870i	−4.43889	−	7.82919i	−15.2846	+	0.396737i
14.16	−2.55194	+	1.67844i	2.99994	−	0.0186225i	2.11093	−	4.89368i	4.95460	−	0.672245i	−7.62442	+	5.08274i	−0.367687	+	3.14577i	0.705188	+	3.99932i	8.99931	−	0.111733i	−11.5155	+	10.0315i
14.17	−2.54349	+	1.67288i	1.39589	−	2.65546i	2.08649	−	4.83703i	0.928281	+	4.91307i	0.891840	+	9.08930i	−1.40607	+	12.0297i	0.670238	+	3.80111i	−5.10298	−	7.41347i	−10.5800	−	10.9434i
14.18	−2.46008	+	1.61802i	0.782436	+	2.89617i	1.84969	−	4.28806i	−4.41522	+	2.34646i	−6.61092	−	5.85881i	−0.637549	+	5.45458i	0.342570	+	1.94281i	−7.77559	+	4.53213i	7.06518	−	12.9164i
14.19	−2.44263	+	1.60654i	−1.03889	−	2.81438i	1.80115	−	4.17553i	4.99900	−	0.0998284i	7.05904	+	5.20546i	0.234503	−	2.00630i	0.277921	+	1.57617i	−6.84142	+	5.84765i	−12.0503	+	8.27496i
14.20	−2.27974	+	1.49941i	0.709430	−	2.91491i	1.36468	−	3.16368i	−3.63481	−	3.43339i	2.75333	+	7.70898i	0.726714	−	6.21743i	−0.262753	−	1.49015i	−7.99342	−	4.13585i	13.4345	+	2.37716i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
81.h	odd	54	1	inner
405.v	odd	54	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	405.3.v.a	✓	1908
5.b	even	2	1	inner	405.3.v.a	✓	1908
81.h	odd	54	1	inner	405.3.v.a	✓	1908
405.v	odd	54	1	inner	405.3.v.a	✓	1908

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
405.3.v.a	✓	1908	1.a	even	1	1	trivial
405.3.v.a	✓	1908	5.b	even	2	1	inner
405.3.v.a	✓	1908	81.h	odd	54	1	inner
405.3.v.a	✓	1908	405.v	odd	54	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(405, [\chi])\).