Newform orbit 532.2.bs.a

• Label: 532.2.bs.a
• Level: $532$
• Weight: $2$
• Character orbit: 532.bs
• Analytic conductor: $4.248$
• Analytic rank: $0$
• Dimension: $456$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	532.bs (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.24804138753\)
Analytic rank:	\(0\)
Dimension:	\(456\)
Relative dimension:	\(76\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 456 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
67.1	−1.41027	−	0.105551i	0.418387	+	2.37279i	1.97772	+	0.297709i	0.679173	+	3.85178i	−0.339589	−	3.39044i	−0.893280	−	2.49039i	−2.75769	−	0.628600i	−2.63601	+	0.959431i	−0.551259	−	5.50374i
67.2	−1.40744	+	0.138242i	−0.482711	−	2.73759i	1.96178	−	0.389136i	−0.420689	−	2.38585i	1.05784	+	3.78626i	0.600818	+	2.57663i	−2.70729	+	0.818886i	−4.44231	+	1.61687i	0.921921	+	3.29978i
67.3	−1.40430	+	0.167132i	0.208081	+	1.18008i	1.94413	−	0.469408i	−0.276151	−	1.56613i	−0.489438	−	1.62242i	2.55554	−	0.684996i	−2.65170	+	0.984118i	1.46978	−	0.534955i	0.649551	+	2.15317i
67.4	−1.40068	−	0.195174i	0.0348539	+	0.197667i	1.92381	+	0.546753i	−0.0701545	−	0.397866i	−0.0102399	−	0.283670i	−2.61049	+	0.430536i	−2.58794	−	1.14130i	2.78122	−	1.01228i	0.0206110	+	0.570976i
67.5	−1.39513	+	0.231553i	0.548755	+	3.11214i	1.89277	−	0.646093i	−0.509909	−	2.89184i	−1.48621	−	4.21477i	−2.07315	−	1.64379i	−2.49105	+	1.33966i	−6.56523	+	2.38955i	1.38100	+	3.91641i
67.6	−1.39343	−	0.241551i	−0.333369	−	1.89063i	1.88331	+	0.673171i	−0.442083	−	2.50718i	0.00784308	+	2.71499i	−1.02107	−	2.44078i	−2.46165	−	1.39293i	−0.644274	+	0.234497i	0.0104008	+	3.60037i
67.7	−1.38767	−	0.272697i	−0.543937	−	3.08482i	1.85127	+	0.756828i	0.563813	+	3.19754i	−0.0864142	+	4.42905i	2.01661	−	1.71269i	−2.36258	−	1.55507i	−6.40116	+	2.32983i	0.0895719	−	4.59089i
67.8	−1.36216	+	0.380143i	−0.356391	−	2.02119i	1.71098	−	1.03563i	0.237205	+	1.34525i	1.25381	+	2.61772i	−1.99423	+	1.73869i	−1.93695	+	2.06112i	−1.13913	+	0.414611i	−0.834501	−	1.74229i
67.9	−1.36106	+	0.384089i	−0.145514	−	0.825249i	1.70495	−	1.04553i	0.299620	+	1.69923i	0.515022	+	1.06732i	1.65820	−	2.06164i	−1.91896	+	2.07789i	2.15922	−	0.785890i	−1.06046	−	2.19767i
67.10	−1.36040	−	0.386412i	0.0663041	+	0.376029i	1.70137	+	1.05135i	0.412864	+	2.34147i	0.0551020	−	0.537170i	1.67864	+	2.04504i	−1.90829	−	2.08768i	2.68208	−	0.976196i	0.343111	−	3.34487i
67.11	−1.26336	+	0.635558i	0.319161	+	1.81005i	1.19213	−	1.60587i	−0.215645	−	1.22298i	−1.55361	−	2.08390i	1.37354	+	2.26128i	−0.485462	+	2.78645i	−0.355354	+	0.129338i	1.04971	+	1.40801i
67.12	−1.22946	−	0.698873i	0.566955	+	3.21536i	1.02315	+	1.71847i	0.00998364	+	0.0566200i	1.55008	−	4.34940i	0.827948	+	2.51287i	−0.0569346	−	2.82785i	−7.19804	+	2.61987i	0.0272957	−	0.0765895i
67.13	−1.21312	+	0.726864i	0.319521	+	1.81209i	0.943336	−	1.76355i	0.536899	+	3.04491i	−1.70476	−	1.96604i	−1.56905	+	2.13028i	0.137480	+	2.82508i	−0.362503	+	0.131940i	−2.86456	−	3.30359i
67.14	−1.19258	−	0.760108i	0.119115	+	0.675535i	0.844473	+	1.81297i	−0.704394	−	3.99482i	0.371426	−	0.896167i	−0.934804	+	2.47510i	0.370957	−	2.80400i	2.37692	−	0.865127i	−2.19645	+	5.29953i
67.15	−1.13275	−	0.846690i	−0.274503	−	1.55678i	0.566233	+	1.91817i	0.639503	+	3.62680i	−1.00717	+	1.99586i	−2.64306	−	0.119203i	0.982697	−	2.65223i	0.470853	−	0.171377i	2.34638	−	4.64971i
67.16	−1.12677	−	0.854627i	0.307607	+	1.74452i	0.539224	+	1.92594i	0.135526	+	0.768607i	1.14432	−	2.22857i	0.496865	−	2.59868i	1.03838	−	2.63093i	−0.129665	+	0.0471940i	0.504166	−	0.981868i
67.17	−1.10911	+	0.877426i	0.0667605	+	0.378617i	0.460247	−	1.94632i	−0.638058	−	3.61860i	−0.406253	−	0.361351i	−2.30030	−	1.30714i	1.19729	+	2.56252i	2.68018	−	0.975507i	3.88273	+	3.45358i
67.18	−1.10687	−	0.880254i	−0.405266	−	2.29838i	0.450305	+	1.94865i	−0.226617	−	1.28521i	−1.57458	+	2.90074i	2.28713	+	1.33005i	1.21688	−	2.55327i	−2.29923	+	0.836852i	−0.880478	+	1.62204i
67.19	−1.10346	+	0.884521i	−0.284110	−	1.61127i	0.435244	−	1.95207i	−0.438232	−	2.48534i	1.73871	+	1.52667i	2.26054	−	1.37476i	1.24637	+	2.53901i	0.303610	−	0.110505i	2.68191	+	2.35484i
67.20	−1.02009	−	0.979500i	−0.146820	−	0.832659i	0.0811614	+	1.99835i	−0.0404366	−	0.229328i	−0.665819	+	0.993196i	2.58800	−	0.549766i	1.87459	−	2.11799i	2.14731	−	0.781558i	−0.183377	+	0.273542i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
133.be	odd	18	1	inner
532.bs	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	532.2.bs.a	✓	456
4.b	odd	2	1	inner	532.2.bs.a	✓	456
7.c	even	3	1		532.2.ce.a	yes	456
19.f	odd	18	1		532.2.ce.a	yes	456
28.g	odd	6	1		532.2.ce.a	yes	456
76.k	even	18	1		532.2.ce.a	yes	456
133.be	odd	18	1	inner	532.2.bs.a	✓	456
532.bs	even	18	1	inner	532.2.bs.a	✓	456

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
532.2.bs.a	✓	456	1.a	even	1	1	trivial
532.2.bs.a	✓	456	4.b	odd	2	1	inner
532.2.bs.a	✓	456	133.be	odd	18	1	inner
532.2.bs.a	✓	456	532.bs	even	18	1	inner
532.2.ce.a	yes	456	7.c	even	3	1
532.2.ce.a	yes	456	19.f	odd	18	1
532.2.ce.a	yes	456	28.g	odd	6	1
532.2.ce.a	yes	456	76.k	even	18	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(532, [\chi])\).