Newform orbit 451.2.cb.a

• Label: 451.2.cb.a
• Level: $451$
• Weight: $2$
• Character orbit: 451.cb
• Analytic conductor: $3.601$
• Analytic rank: $0$
• Dimension: $640$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 451 = 11 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	451.cb (of order \(40\), degree \(16\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.60125313116\)
Analytic rank:	\(0\)
Dimension:	\(640\)
Relative dimension:	\(40\) over \(\Q(\zeta_{40})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 640 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 12 q^{5} - 20 q^{6} - 20 q^{7} - 60 q^{8} + 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−2.45706	−	1.25193i	0.264593	−	0.225984i	3.29424	+	4.53413i	0.400139	+	0.203881i	−0.933037	+	0.224002i	−2.57138	+	1.06510i	−1.55493	−	9.81745i	−0.450363	+	2.84348i	−0.727920	−	1.00190i
19.2	−2.27362	−	1.15847i	−2.14149	+	1.82900i	2.65172	+	3.64978i	−3.15714	−	1.60864i	6.98776	−	1.67761i	−0.195383	+	0.0809303i	−1.00249	−	6.32949i	0.771412	−	4.87050i	5.31456	+	7.31487i
19.3	−2.25768	−	1.15034i	−1.54137	+	1.31645i	2.59824	+	3.57617i	1.81595	+	0.925273i	4.99427	−	1.19902i	2.81431	−	1.16573i	−0.959395	−	6.05738i	0.173463	−	1.09520i	−3.03544	−	4.17793i
19.4	−2.24399	−	1.14337i	1.56549	−	1.33705i	2.55263	+	3.51339i	2.13368	+	1.08717i	−5.04168	+	1.21040i	2.17793	−	0.902129i	−0.923011	−	5.82766i	0.193737	−	1.22321i	−3.54493	−	4.87918i
19.5	−2.10797	−	1.07406i	1.07504	−	0.918167i	2.11436	+	2.91016i	−3.41581	−	1.74044i	−3.25231	+	0.780812i	−2.40877	+	0.997745i	−0.591103	−	3.73208i	−0.156633	+	0.988941i	5.33108	+	7.33760i
19.6	−1.91419	−	0.975326i	0.549329	−	0.469171i	1.53727	+	2.11588i	−2.43453	−	1.24045i	−1.50911	+	0.362306i	4.34299	−	1.79893i	−0.206809	−	1.30574i	−0.387663	+	2.44761i	3.45029	+	4.74892i
19.7	−1.77544	−	0.904634i	−1.66381	+	1.42102i	1.15827	+	1.59422i	1.78317	+	0.908570i	4.23950	−	1.01781i	−4.73760	+	1.96238i	0.00917587	+	0.0579342i	0.279636	−	1.76556i	−2.34399	−	3.22623i
19.8	−1.67954	−	0.855770i	1.62971	−	1.39190i	0.912954	+	1.25657i	3.46600	+	1.76601i	−3.92831	+	0.943104i	−3.51248	+	1.45492i	0.131749	+	0.831828i	0.249252	−	1.57371i	−4.30999	−	5.93219i
19.9	−1.60079	−	0.815643i	0.330467	−	0.282245i	0.721681	+	0.993309i	−0.389196	−	0.198305i	−0.759219	+	0.182272i	0.561651	−	0.232643i	0.217029	+	1.37026i	−0.439757	+	2.77652i	0.461274	+	0.634889i
19.10	−1.38757	−	0.707002i	−0.835263	+	0.713382i	0.249926	+	0.343994i	−2.01528	−	1.02684i	1.66335	−	0.399334i	−2.57395	+	1.06616i	0.383647	+	2.42225i	−0.280553	+	1.77134i	2.07037	+	2.84961i
19.11	−1.36597	−	0.695997i	1.99186	−	1.70121i	0.205894	+	0.283389i	0.106180	+	0.0541016i	−3.90486	+	0.937473i	2.40073	−	0.994415i	0.395641	+	2.49798i	0.604089	−	3.81407i	−0.107385	−	0.147802i
19.12	−1.34536	−	0.685496i	2.26470	−	1.93424i	0.164522	+	0.226445i	−1.26968	−	0.646937i	−4.37276	+	1.04981i	−2.95754	+	1.22505i	0.406297	+	2.56526i	0.918298	−	5.79790i	1.26471	+	1.74073i
19.13	−1.30127	−	0.663030i	−1.41349	+	1.20723i	0.0781247	+	0.107529i	3.73012	+	1.90059i	2.63976	−	0.633751i	1.78086	−	0.737658i	0.426563	+	2.69321i	0.0712337	−	0.449752i	−3.59375	−	4.94637i
19.14	−1.26138	−	0.642703i	−2.61999	+	2.23768i	0.00243219	+	0.00334762i	−0.418375	−	0.213173i	4.74295	−	1.13868i	0.466057	−	0.193047i	0.442005	+	2.79071i	1.38781	−	8.76232i	0.390721	+	0.537782i
19.15	−0.986678	−	0.502738i	−1.46321	+	1.24970i	−0.454782	−	0.625953i	−1.06992	−	0.545149i	2.07199	−	0.497440i	3.92120	−	1.62422i	0.480496	+	3.03373i	0.109931	−	0.694075i	0.781595	+	1.07577i
19.16	−0.817915	−	0.416749i	0.193493	−	0.165259i	−0.680265	−	0.936304i	2.43833	+	1.24239i	−0.227132	+	0.0545297i	1.84431	−	0.763937i	0.453399	+	2.86265i	−0.459174	+	2.89911i	−1.47658	−	2.03234i
19.17	−0.701235	−	0.357297i	0.368292	−	0.314551i	−0.811501	−	1.11694i	0.0645218	+	0.0328755i	−0.370647	+	0.0889845i	−1.66801	+	0.690911i	0.416208	+	2.62783i	−0.432607	+	2.73137i	−0.0334986	−	0.0461069i
19.18	−0.365136	−	0.186046i	−1.46027	+	1.24719i	−1.07686	−	1.48217i	−3.22303	−	1.64221i	0.765234	−	0.183716i	−0.377163	+	0.156226i	0.245662	+	1.55105i	0.107609	−	0.679418i	0.871316	+	1.19926i
19.19	−0.204533	−	0.104215i	2.15752	−	1.84270i	−1.14460	−	1.57540i	−1.81441	−	0.924489i	−0.633319	+	0.152047i	2.62645	−	1.08791i	0.141747	+	0.894958i	0.790061	−	4.98825i	0.274761	+	0.378176i
19.20	−0.106150	−	0.0540863i	−1.47782	+	1.26217i	−1.16723	−	1.60655i	1.94674	+	0.991912i	0.225137	−	0.0540507i	−2.87571	+	1.19116i	0.0742830	+	0.469005i	0.121554	−	0.767461i	−0.152998	−	0.210584i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
451.cb	even	40	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	451.2.cb.a	yes	640
11.d	odd	10	1		451.2.bz.a	✓	640
41.h	odd	40	1		451.2.bz.a	✓	640
451.cb	even	40	1	inner	451.2.cb.a	yes	640

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
451.2.bz.a	✓	640	11.d	odd	10	1
451.2.bz.a	✓	640	41.h	odd	40	1
451.2.cb.a	yes	640	1.a	even	1	1	trivial
451.2.cb.a	yes	640	451.cb	even	40	1	inner

Hecke kernels

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