Newform orbit 456.2.bj.a

• Label: 456.2.bj.a
• Level: $456$
• Weight: $2$
• Character orbit: 456.bj
• Analytic conductor: $3.641$
• Analytic rank: $0$
• Dimension: $456$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bj (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.64117833217\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 456 q - 6 q^{4} - 6 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
29.1	−1.40913	−	0.119802i	1.54023	+	0.792268i	1.97130	+	0.337632i	−2.20694	−	0.803259i	−2.07547	−	1.30093i	0.552347	−	0.956693i	−2.73736	−	0.711932i	1.74462	+	2.44055i	3.01363	+	1.39629i
29.2	−1.40830	+	0.129239i	1.70418	−	0.309442i	1.96659	−	0.364014i	2.55208	+	0.928880i	−2.36000	+	0.656033i	−0.202591	+	0.350898i	−2.72250	+	0.766800i	2.80849	−	1.05469i	−3.71413	−	0.978310i
29.3	−1.40371	+	0.172030i	0.659671	−	1.60151i	1.94081	−	0.482961i	0.422928	+	0.153933i	−0.650481	+	2.36154i	−1.57343	+	2.72525i	−2.64126	+	1.01182i	−2.12967	−	2.11294i	−0.620150	−	0.143322i
29.4	−1.40256	−	0.181161i	−1.22184	−	1.22764i	1.93436	+	0.508180i	−0.605934	−	0.220542i	1.49130	+	1.94320i	−0.0172903	+	0.0299477i	−2.62100	−	1.06319i	−0.0142192	+	2.99997i	0.809907	+	0.419096i
29.5	−1.37789	+	0.318442i	−1.69173	+	0.371550i	1.79719	−	0.877560i	0.422928	+	0.153933i	2.21271	−	1.05068i	−1.57343	+	2.72525i	−2.19689	+	1.78149i	2.72390	−	1.25713i	−0.631769	−	0.0774256i
29.6	−1.37734	−	0.320835i	−0.458024	+	1.67039i	1.79413	+	0.883797i	0.810544	+	0.295014i	1.16677	−	2.15375i	1.30689	−	2.26359i	−2.18757	−	1.79291i	−2.58043	−	1.53016i	−1.02174	−	0.666385i
29.7	−1.36999	−	0.350891i	0.00879937	−	1.73203i	1.75375	+	0.961436i	3.53507	+	1.28666i	−0.619809	+	2.36978i	2.12851	−	3.68669i	−2.06526	−	1.93253i	−2.99985	−	0.0304815i	−4.39153	−	3.00314i
29.8	−1.36757	+	0.360220i	−0.600669	+	1.62456i	1.74048	−	0.985252i	2.55208	+	0.928880i	0.236256	−	2.43807i	−0.202591	+	0.350898i	−2.02532	+	1.97436i	−2.27839	−	1.95165i	−3.82474	−	0.350996i
29.9	−1.33994	−	0.452277i	−1.18246	+	1.26562i	1.59089	+	1.21205i	−3.53707	−	1.28739i	2.15684	−	1.16106i	−2.18566	+	3.78568i	−1.58352	−	2.34360i	−0.203576	−	2.99308i	4.15722	+	3.32476i
29.10	−1.28506	−	0.590445i	0.956494	+	1.44399i	1.30275	+	1.51751i	2.00808	+	0.730881i	−0.376551	−	2.42037i	−1.92113	+	3.32750i	−0.778098	−	2.71929i	−1.17024	+	2.76234i	−2.14895	−	2.12489i
29.11	−1.28317	+	0.594528i	0.512773	+	1.65441i	1.29307	−	1.52577i	−2.20694	−	0.803259i	−1.64157	−	1.81804i	0.552347	−	0.956693i	−0.752130	+	2.72659i	−2.47413	+	1.69667i	3.30945	−	0.281363i
29.12	−1.25602	+	0.649940i	−0.996823	−	1.41645i	1.15515	−	1.63267i	−0.605934	−	0.220542i	2.17264	+	1.13121i	−0.0172903	+	0.0299477i	−0.389754	+	2.80144i	−1.01269	+	2.82391i	0.904403	−	0.116817i
29.13	−1.18454	+	0.772564i	1.72455	−	0.161004i	0.806290	−	1.83027i	0.810544	+	0.295014i	−1.91842	+	1.52304i	1.30689	−	2.26359i	0.458916	+	2.79095i	2.94816	−	0.555321i	−1.18804	+	0.276740i
29.14	−1.17817	−	0.782243i	1.25775	−	1.19082i	0.776191	+	1.84324i	−1.78566	−	0.649926i	−2.41337	+	0.419129i	0.802436	−	1.38986i	0.527373	−	2.77883i	0.163881	−	2.99552i	1.59541	+	2.16254i
29.15	−1.16736	+	0.798295i	−1.70724	−	0.292098i	0.725452	−	1.86379i	3.53507	+	1.28666i	2.22614	−	1.02190i	2.12851	−	3.68669i	0.640993	+	2.75484i	2.82936	+	0.997364i	−5.15382	+	1.32003i
29.16	−1.13710	−	0.840837i	−1.68083	−	0.418104i	0.585985	+	1.91223i	−1.06583	−	0.387929i	1.55971	+	1.88873i	0.936243	−	1.62162i	0.941551	−	2.66711i	2.65038	+	1.40552i	0.885765	+	1.33730i
29.17	−1.10445	+	0.883289i	1.45172	−	0.944724i	0.439602	−	1.95109i	−3.53707	−	1.28739i	−0.768885	+	2.32569i	−2.18566	+	3.78568i	1.23786	+	2.54317i	1.21499	−	2.74295i	5.04364	−	1.70240i
29.18	−1.02199	−	0.977517i	0.256721	−	1.71292i	0.0889204	+	1.99802i	0.523431	+	0.190513i	−1.93677	+	1.49963i	−2.04421	+	3.54067i	1.86223	−	2.12888i	−2.86819	−	0.879485i	−0.348711	−	0.706365i
29.19	−1.02056	−	0.979010i	−1.50352	+	0.859896i	0.0830780	+	1.99827i	2.94303	+	1.07118i	2.37628	+	0.594389i	−0.245385	+	0.425019i	1.87154	−	2.12069i	1.52116	−	2.58575i	−1.95484	−	3.97446i
29.20	−1.00562	+	0.994353i	1.25596	+	1.19271i	0.0225244	−	1.99987i	2.00808	+	0.730881i	−2.44899	+	0.0494634i	−1.92113	+	3.32750i	1.96593	+	2.03350i	0.154887	+	2.99600i	−2.74611	+	1.26175i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
8.b	even	2	1	inner
19.f	odd	18	1	inner
24.h	odd	2	1	inner
57.j	even	18	1	inner
152.s	odd	18	1	inner
456.bj	even	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	456.2.bj.a	✓	456
3.b	odd	2	1	inner	456.2.bj.a	✓	456
8.b	even	2	1	inner	456.2.bj.a	✓	456
19.f	odd	18	1	inner	456.2.bj.a	✓	456
24.h	odd	2	1	inner	456.2.bj.a	✓	456
57.j	even	18	1	inner	456.2.bj.a	✓	456
152.s	odd	18	1	inner	456.2.bj.a	✓	456
456.bj	even	18	1	inner	456.2.bj.a	✓	456

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
456.2.bj.a	✓	456	1.a	even	1	1	trivial
456.2.bj.a	✓	456	3.b	odd	2	1	inner
456.2.bj.a	✓	456	8.b	even	2	1	inner
456.2.bj.a	✓	456	19.f	odd	18	1	inner
456.2.bj.a	✓	456	24.h	odd	2	1	inner
456.2.bj.a	✓	456	57.j	even	18	1	inner
456.2.bj.a	✓	456	152.s	odd	18	1	inner
456.2.bj.a	✓	456	456.bj	even	18	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(456, [\chi])\).