Newform orbit 451.2.j.a

• Label: 451.2.j.a
• Level: $451$
• Weight: $2$
• Character orbit: 451.j
• 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.j (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.

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
119.1	−0.849627	−	2.61488i	0.959252	−	0.696937i	−4.49771	+	3.26778i	2.40698			−2.63741	−	1.91619i	1.34961	+	4.15366i	7.91752	+	5.75241i	−0.492609	+	1.51609i	−2.04503	−	6.29397i
119.2	−0.829700	−	2.55355i	−2.14723	+	1.56006i	−4.21420	+	3.06179i	2.44348			5.76524	+	4.18869i	−1.44607	−	4.45056i	6.97060	+	5.06444i	1.24978	−	3.84644i	−2.02735	−	6.23956i
119.3	−0.804515	−	2.47604i	0.229091	−	0.166445i	−3.86551	+	2.80846i	−1.16972			−0.596431	−	0.433333i	−0.525573	−	1.61755i	5.85124	+	4.25117i	−0.902272	+	2.77691i	0.941054	+	2.89627i
119.4	−0.750714	−	2.31046i	−1.61367	+	1.17240i	−3.15662	+	2.29342i	−1.06432			3.92019	+	2.84819i	0.313070	+	0.963529i	3.73778	+	2.71566i	0.302360	−	0.930569i	0.798997	+	2.45906i
119.5	−0.693294	−	2.13374i	0.846064	−	0.614701i	−2.45416	+	1.78305i	−2.73407			−1.89818	−	1.37911i	−0.397082	−	1.22209i	1.87588	+	1.36291i	−0.589085	+	1.81302i	1.89552	+	5.83380i
119.6	−0.669819	−	2.06149i	2.66720	−	1.93784i	−2.18305	+	1.58608i	3.00400			−5.78137	−	4.20041i	−0.229210	−	0.705437i	1.22471	+	0.889805i	2.43171	−	7.48404i	−2.01213	−	6.19271i
119.7	−0.656273	−	2.01980i	1.74804	−	1.27003i	−2.03087	+	1.47551i	−0.276386			−3.71240	−	2.69721i	−0.547003	−	1.68350i	0.876754	+	0.636999i	0.515633	−	1.58696i	0.181384	+	0.558244i
119.8	−0.588450	−	1.81106i	−0.709765	+	0.515675i	−1.31565	+	0.955873i	2.11900			1.35158	+	0.981982i	0.945598	+	2.91025i	−0.575828	−	0.418363i	−0.689205	+	2.12115i	−1.24693	−	3.83765i
119.9	−0.581367	−	1.78926i	−1.54407	+	1.12183i	−1.24544	+	0.904867i	0.571061			2.90492	+	2.11055i	0.502958	+	1.54795i	−0.700972	−	0.509286i	0.198591	−	0.611200i	−0.331996	−	1.02178i
119.10	−0.506048	−	1.55746i	−2.55608	+	1.85710i	−0.551548	+	0.400723i	−4.00839			4.18585	+	3.04120i	−0.366381	−	1.12760i	−1.74648	−	1.26889i	2.15767	−	6.64064i	2.02844	+	6.24289i
119.11	−0.432108	−	1.32989i	0.00678623	−	0.00493049i	0.0361382	−	0.0262559i	−3.32023			−0.00948941	−	0.00689446i	1.12125	+	3.45084i	−2.31308	−	1.68055i	−0.927029	+	2.85310i	1.43470	+	4.41554i
119.12	−0.403344	−	1.24136i	0.485768	−	0.352931i	0.239734	−	0.174177i	2.56069			−0.634048	−	0.460663i	−1.17305	−	3.61027i	−2.42485	−	1.76176i	−0.815641	+	2.51028i	−1.03284	−	3.17875i
119.13	−0.393442	−	1.21089i	−1.19498	+	0.868205i	0.306574	−	0.222739i	−0.976790			1.52146	+	1.10540i	−1.40510	−	4.32444i	−2.45042	−	1.78034i	−0.252850	+	0.778194i	0.384310	+	1.18279i
119.14	−0.391670	−	1.20544i	1.62154	−	1.17812i	0.318362	−	0.231303i	1.86929			−2.05525	−	1.49323i	0.989454	+	3.04523i	−2.45433	−	1.78317i	0.314379	−	0.967559i	−0.732143	−	2.25331i
119.15	−0.324738	−	0.999440i	−2.54516	+	1.84916i	0.724608	−	0.526459i	4.16177			2.67464	+	1.94324i	0.00962619	+	0.0296264i	−2.46182	−	1.78862i	2.13136	−	6.55965i	−1.35148	−	4.15944i
119.16	−0.224956	−	0.692342i	2.01197	−	1.46178i	1.18930	−	0.864078i	−3.11917			−1.46466	−	1.06414i	−1.00727	−	3.10005i	−2.04366	−	1.48481i	0.984173	−	3.02897i	0.701675	+	2.15953i
119.17	−0.163820	−	0.504186i	−1.74772	+	1.26980i	1.39067	−	1.01038i	−0.466136			0.926526	+	0.673161i	0.0711135	+	0.218865i	−1.59501	−	1.15884i	0.515107	−	1.58534i	0.0763625	+	0.235020i
119.18	−0.156122	−	0.480495i	1.08428	−	0.787777i	1.41153	−	1.02554i	2.60184			−0.547804	−	0.398003i	−0.0914884	−	0.281572i	−1.53061	−	1.11205i	−0.371975	+	1.14482i	−0.406205	−	1.25017i
119.19	−0.0968824	−	0.298173i	2.22490	−	1.61648i	1.53851	−	1.11779i	−0.434805			−0.697546	−	0.506797i	0.739025	+	2.27449i	−0.989635	−	0.719012i	1.41010	−	4.33985i	0.0421250	+	0.129647i
119.20	−0.0932370	−	0.286954i	0.0497598	−	0.0361526i	1.54438	−	1.12206i	−3.25835			−0.0150136	−	0.0109080i	−0.0963697	−	0.296595i	−0.954169	−	0.693244i	−0.925882	+	2.84957i	0.303799	+	0.934996i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
451.j	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.j.a	yes	160
11.c	even	5	1		451.2.h.a	✓	160
41.d	even	5	1		451.2.h.a	✓	160
451.j	even	5	1	inner	451.2.j.a	yes	160

    

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

Hecke kernels

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