Newform orbit 451.2.i.a

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

\(\operatorname{Tr}(f)(q) = \) \( 160 q + q^{2} - 7 q^{3} - 39 q^{4} - q^{5} - 4 q^{6} - q^{7} + 13 q^{8} - 45 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
92.1	−0.842068	−	2.59162i	0.696164	−	2.14257i	−4.38937	+	3.18906i	−2.31538	−	1.68223i	−6.13895			−0.729236	−	0.529821i	7.55186	+	5.48675i	−1.67892	−	1.21981i	−2.40997	+	7.41714i
92.2	−0.839651	−	2.58418i	0.292882	−	0.901399i	−4.35494	+	3.16405i	1.73039	+	1.25720i	−2.57530			0.384134	+	0.279090i	7.43663	+	5.40303i	1.70031	+	1.23535i	1.79591	−	5.52726i
92.3	−0.793471	−	2.44205i	−0.860535	+	2.64845i	−3.71599	+	2.69982i	−2.43088	−	1.76614i	7.15047			−3.20031	−	2.32516i	5.38697	+	3.91386i	−3.84674	−	2.79482i	−2.38417	+	7.33773i
92.4	−0.763478	−	2.34974i	−0.962523	+	2.96234i	−3.32036	+	2.41238i	2.50605	+	1.82075i	7.69561			2.43581	+	1.76972i	4.20588	+	3.05575i	−5.42197	−	3.93929i	2.36498	−	7.27867i
92.5	−0.756083	−	2.32698i	−0.302913	+	0.932271i	−3.22516	+	2.34321i	−1.51310	−	1.09933i	2.39841			3.07202	+	2.23195i	3.93221	+	2.85692i	1.64968	+	1.19856i	−1.41410	+	4.35215i
92.6	−0.691482	−	2.12816i	−0.220233	+	0.677809i	−2.43289	+	1.76760i	0.204155	+	0.148327i	1.59477			−0.348300	−	0.253054i	1.82339	+	1.32477i	2.01613	+	1.46480i	0.174495	−	0.537039i
92.7	−0.674368	−	2.07549i	−0.0279669	+	0.0860732i	−2.23486	+	1.62372i	1.55455	+	1.12944i	0.197504			−3.62171	−	2.63133i	1.34610	+	0.977996i	2.42042	+	1.75854i	1.29581	−	3.98811i
92.8	−0.646794	−	1.99063i	0.676790	−	2.08294i	−1.92622	+	1.39948i	3.15354	+	2.29118i	−4.58411			2.98019	+	2.16523i	0.645047	+	0.468654i	−1.45356	−	1.05607i	2.52120	−	7.75945i
92.9	−0.562682	−	1.73176i	0.911370	−	2.80491i	−1.06433	+	0.773284i	−0.951697	−	0.691448i	−5.37023			1.92229	+	1.39663i	−1.00822	−	0.732513i	−4.60987	−	3.34926i	−0.661918	+	2.03717i
92.10	−0.519831	−	1.59988i	0.549267	−	1.69047i	−0.671343	+	0.487759i	−2.72703	−	1.98130i	−2.99007			−0.147834	−	0.107407i	−1.59253	−	1.15704i	−0.128942	−	0.0936821i	−1.75224	+	5.39284i
92.11	−0.494383	−	1.52155i	−0.300693	+	0.925437i	−0.452678	+	0.328890i	−2.92686	−	2.12648i	1.55676			−0.698800	−	0.507708i	−1.86440	−	1.35457i	1.66103	+	1.20681i	−1.78857	+	5.50467i
92.12	−0.460895	−	1.41849i	−0.596115	+	1.83465i	−0.181655	+	0.131980i	3.15372	+	2.29131i	2.87718			−1.13372	−	0.823692i	−2.14234	−	1.55650i	−0.583549	−	0.423973i	1.79667	−	5.52958i
92.13	−0.445428	−	1.37089i	0.626098	−	1.92693i	−0.0628869	+	0.0456900i	0.143816	+	0.104489i	−2.92048			−4.02345	−	2.92321i	−2.24164	−	1.62865i	−0.894019	−	0.649542i	0.0791823	−	0.243698i
92.14	−0.350156	−	1.07767i	0.233897	−	0.719860i	0.579271	−	0.420865i	1.00602	+	0.730914i	−0.857672			0.823426	+	0.598254i	−2.48983	−	1.80897i	1.96356	+	1.42661i	0.435421	−	1.34009i
92.15	−0.317310	−	0.976580i	−0.272240	+	0.837867i	0.765011	−	0.555813i	1.22814	+	0.892298i	0.904629			3.03514	+	2.20516i	−2.44700	−	1.77785i	1.79914	+	1.30715i	0.481698	−	1.48251i
92.16	−0.268311	−	0.825775i	−0.984882	+	3.03116i	1.00812	−	0.732442i	−0.165526	−	0.120262i	2.76731			−1.72289	−	1.25175i	−2.28021	−	1.65667i	−5.79086	−	4.20730i	−0.0548967	+	0.168955i
92.17	−0.156942	−	0.483018i	−0.858828	+	2.64320i	1.40936	−	1.02396i	−2.04169	−	1.48337i	1.41150			3.85897	+	2.80370i	−1.53754	−	1.11709i	−3.82188	−	2.77676i	−0.396069	+	1.21898i
92.18	−0.143433	−	0.441442i	0.782162	−	2.40725i	1.44374	−	1.04894i	3.29473	+	2.39376i	−1.17485			−1.37868	−	1.00167i	−1.42115	−	1.03253i	−2.75600	−	2.00235i	0.584134	−	1.79778i
92.19	−0.105289	−	0.324046i	−0.319595	+	0.983612i	1.52411	−	1.10733i	−2.55694	−	1.85773i	0.352385			−0.00278535	−	0.00202368i	−1.07060	−	0.777836i	1.56170	+	1.13464i	−0.332772	+	1.02417i
92.20	−0.0632899	−	0.194786i	0.208225	−	0.640850i	1.58410	−	1.15091i	0.219710	+	0.159629i	−0.138007			1.75581	+	1.27567i	−0.655830	−	0.476489i	2.05972	+	1.49647i	0.0171881	−	0.0528994i

Inner twists

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

    

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

Hecke kernels

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