Newform orbit 451.2.h.a

• Label: 451.2.h.a
• Level: $451$
• Weight: $2$
• Character orbit: 451.h
• Analytic conductor: $3.601$
• Analytic rank: $0$
• Dimension: $160$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 451 = 11 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	451.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.60125313116\)
Analytic rank:	\(0\)
Dimension:	\(160\)
Relative dimension:	\(40\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 160 q + q^{2} - 7 q^{3} - 39 q^{4} - q^{5} - 4 q^{6} - 6 q^{7} + 3 q^{8} - 45 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
59.1	−0.865501	+	2.66374i	0.258258	−	0.794835i	−4.72838	−	3.43537i	−0.276609	+	0.851316i	1.89371	+	1.37586i	1.68843			8.71151	−	6.32928i	1.86198	+	1.35281i	−2.02828	−	1.47363i
59.2	−0.817873	+	2.51715i	−1.03453	+	3.18397i	−4.04912	−	2.94186i	1.18570	−	3.64922i	−7.16842	−	5.20816i	−0.357977			6.43434	−	4.67482i	−6.64032	−	4.82448i	8.21590	+	5.96920i
59.3	−0.751623	+	2.31326i	−0.563723	+	1.73496i	−3.16819	−	2.30182i	−0.848204	+	2.61050i	−3.58970	−	2.60807i	−4.32358			3.77044	−	2.73938i	−0.265257	−	0.192721i	−5.40123	−	3.92422i
59.4	−0.746065	+	2.29615i	−0.0930617	+	0.286414i	−3.09767	−	2.25059i	0.524330	−	1.61372i	−0.588221	−	0.427368i	−0.287887			3.57231	−	2.59543i	2.35368	+	1.71005i	3.31416	+	2.40788i
59.5	−0.716192	+	2.20421i	0.439099	−	1.35141i	−2.72758	−	1.98170i	0.222886	−	0.685972i	2.66431	+	1.93573i	−0.896580			2.57154	−	1.86833i	0.793555	+	0.576551i	1.35240	+	0.982575i
59.6	−0.682125	+	2.09936i	0.847891	−	2.60954i	−2.32400	−	1.68849i	−0.661943	+	2.03725i	4.90001	+	3.56007i	2.50637			1.55836	−	1.13221i	−3.66373	−	2.66186i	−3.82540	−	2.77932i
59.7	−0.603793	+	1.85828i	−0.444328	+	1.36750i	−1.47062	−	1.06846i	0.243892	−	0.750623i	−2.27292	−	1.65137i	4.75408			−0.288042	+	0.209275i	0.754421	+	0.548119i	1.24761	+	0.906441i
59.8	−0.602884	+	1.85548i	0.864312	−	2.66008i	−1.46132	−	1.06171i	1.15183	−	3.54497i	4.41465	+	3.20743i	3.75276			−0.305743	+	0.222135i	−3.90193	−	2.83492i	5.88321	+	4.27440i
59.9	−0.564265	+	1.73663i	−0.480257	+	1.47808i	−1.07945	−	0.784268i	0.115478	−	0.355406i	−2.29588	−	1.66806i	−2.50820			−0.983451	+	0.714519i	0.472981	+	0.343641i	0.552048	+	0.401086i
59.10	−0.527489	+	1.62344i	0.911798	−	2.80623i	−0.739295	−	0.537129i	−0.249725	+	0.768576i	4.07479	+	2.96051i	−4.89487			−1.50000	+	1.08981i	−4.61648	−	3.35407i	−1.11601	−	0.810831i
59.11	−0.520664	+	1.60244i	−0.0238513	+	0.0734068i	−0.678688	−	0.493095i	−1.28362	+	3.95058i	−0.105211	−	0.0764406i	3.27479			−1.58271	+	1.14991i	2.42223	+	1.75985i	−5.66223	−	4.11385i
59.12	−0.472524	+	1.45428i	−1.00332	+	3.08789i	−0.273616	−	0.198794i	−0.450992	+	1.38801i	−4.01657	−	2.91821i	1.39505			−2.05578	+	1.49361i	−6.10139	−	4.43292i	−1.80545	−	1.31174i
59.13	−0.354023	+	1.08957i	0.289073	−	0.889675i	0.556200	+	0.404103i	−0.219575	+	0.675783i	0.867026	+	0.629932i	−1.60325			−2.49090	+	1.80974i	1.71909	+	1.24899i	−0.658579	−	0.478486i
59.14	−0.343347	+	1.05671i	0.00286704	−	0.00882385i	0.619281	+	0.449934i	−0.934433	+	2.87589i	0.00833988	+	0.00605928i	−0.743893			−2.48586	+	1.80609i	2.42698	+	1.76331i	−2.71815	−	1.97485i
59.15	−0.304700	+	0.937771i	−0.536191	+	1.65023i	0.831461	+	0.604092i	1.20405	−	3.70567i	−1.38416	−	1.00565i	2.21455			−2.41528	+	1.75480i	−0.00869851	−	0.00631984i	3.10820	+	2.25824i
59.16	−0.290884	+	0.895249i	0.570751	−	1.75659i	0.901177	+	0.654743i	0.681666	−	2.09795i	1.40656	+	1.02193i	−0.0867938			−2.37138	+	1.72291i	−0.332807	−	0.241799i	1.67990	+	1.22052i
59.17	−0.188776	+	0.580994i	−0.840906	+	2.58804i	1.31612	+	0.956215i	−0.445195	+	1.37017i	−1.34489	−	0.977123i	−1.32885			−1.79245	+	1.30229i	−3.56380	−	2.58925i	−0.712018	−	0.517311i
59.18	−0.108343	+	0.333446i	0.410604	−	1.26371i	1.51859	+	1.10332i	0.384326	−	1.18283i	0.376892	+	0.273828i	3.96486			−1.09972	+	0.798991i	0.998684	+	0.725586i	0.352772	+	0.256304i
59.19	−0.0675881	+	0.208015i	−0.558994	+	1.72041i	1.57933	+	1.14745i	0.679232	−	2.09046i	−0.320088	−	0.232558i	−2.97826			−0.699327	+	0.508091i	−0.220271	−	0.160036i	0.388939	+	0.282581i
59.20	−0.0280571	+	0.0863508i	0.851349	−	2.62018i	1.61136	+	1.17073i	−0.786348	+	2.42013i	0.202369	+	0.147029i	1.24130			−0.293212	+	0.213031i	−3.71351	−	2.69803i	−0.186918	−	0.135804i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
451.h	even	5	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	451.2.h.a	✓	160
11.c	even	5	1		451.2.j.a	yes	160
41.d	even	5	1		451.2.j.a	yes	160
451.h	even	5	1	inner	451.2.h.a	✓	160

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
451.2.h.a	✓	160	1.a	even	1	1	trivial
451.2.h.a	✓	160	451.h	even	5	1	inner
451.2.j.a	yes	160	11.c	even	5	1
451.2.j.a	yes	160	41.d	even	5	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(451, [\chi])\).