Newform orbit 451.2.bp.a

• Label: 451.2.bp.a
• Level: $451$
• Weight: $2$
• Character orbit: 451.bp
• Analytic conductor: $3.601$
• Analytic rank: $0$
• Dimension: $320$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 451 = 11 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	451.bp (of order \(20\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.60125313116\)
Analytic rank:	\(0\)
Dimension:	\(320\)
Relative dimension:	\(40\) over \(\Q(\zeta_{20})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 320 q - 10 q^{2} - 2 q^{3} + 74 q^{4} - 10 q^{5} + 12 q^{6} - 6 q^{7} - 30 q^{8} + 30 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1	−1.60991	+	2.21585i	−0.271766	−	1.71586i	−1.70015	−	5.23254i	2.29533	−	3.15925i	4.23961	+	2.16019i	−1.82755	−	1.82755i	9.12185	+	2.96387i	−0.0171547	+	0.00557389i	3.30516	+	10.1722i
5.2	−1.52507	+	2.09909i	0.127643	+	0.805905i	−1.46227	−	4.50041i	−0.326897	+	0.449935i	−1.88633	−	0.961132i	0.919207	+	0.919207i	6.74158	+	2.19047i	2.21998	−	0.721315i	−0.445910	−	1.37237i
5.3	−1.44854	+	1.99375i	0.209907	+	1.32530i	−1.25872	−	3.87395i	0.631271	−	0.868870i	−2.94637	−	1.50125i	0.638542	+	0.638542i	4.85943	+	1.57892i	1.14082	−	0.370674i	0.817886	+	2.51719i
5.4	−1.42955	+	1.96760i	−0.190664	−	1.20380i	−1.20982	−	3.72344i	−2.30106	+	3.16714i	2.64117	+	1.34574i	2.03595	+	2.03595i	4.42963	+	1.43927i	1.44038	−	0.468007i	−2.94220	−	9.05515i
5.5	−1.41048	+	1.94136i	−0.349144	−	2.20441i	−1.16140	−	3.57441i	−1.03708	+	1.42742i	4.77203	+	2.43147i	−2.05883	−	2.05883i	4.01295	+	1.30389i	−1.88435	+	0.612263i	−1.30835	−	4.02670i
5.6	−1.28640	+	1.77058i	−0.478504	−	3.02116i	−0.862096	−	2.65326i	0.687720	−	0.946565i	5.96476	+	3.03920i	3.02431	+	3.02431i	1.64393	+	0.534145i	−6.04524	+	1.96422i	0.791287	+	2.43533i
5.7	−1.14012	+	1.56924i	0.418883	+	2.64473i	−0.544601	−	1.67611i	−2.01627	+	2.77515i	−4.62777	−	2.35797i	1.86813	+	1.86813i	−0.438377	−	0.142437i	−3.96594	+	1.28861i	−2.05609	−	6.32799i
5.8	−1.09352	+	1.50511i	−0.177959	−	1.12359i	−0.451516	−	1.38962i	1.27493	−	1.75480i	1.88572	+	0.960821i	2.72975	+	2.72975i	−0.953443	−	0.309792i	1.62239	−	0.527148i	1.24698	+	3.83782i
5.9	−1.07194	+	1.47540i	0.303578	+	1.91671i	−0.409712	−	1.26096i	2.33885	−	3.21916i	−3.15333	−	1.60670i	−3.51797	−	3.51797i	−1.16926	−	0.379916i	−0.728466	+	0.236693i	2.24243	+	6.90149i
5.10	−1.03235	+	1.42091i	−0.153541	−	0.969422i	−0.335199	−	1.03164i	−0.754918	+	1.03905i	1.53597	+	0.782615i	−2.03761	−	2.03761i	−1.52885	−	0.496754i	1.93697	−	0.629358i	−0.697062	−	2.14534i
5.11	−0.943608	+	1.29877i	0.325536	+	2.05535i	−0.178361	−	0.548938i	−0.906618	+	1.24785i	−2.97660	−	1.51665i	−1.35872	−	1.35872i	−2.17234	−	0.705835i	−1.26532	+	0.411128i	−0.765176	−	2.35497i
5.12	−0.880989	+	1.21258i	0.121313	+	0.765942i	−0.0761683	−	0.234422i	1.69135	−	2.32794i	−1.03564	−	0.527685i	1.34045	+	1.34045i	−2.49958	−	0.812164i	2.28122	−	0.741213i	1.33275	+	4.10178i
5.13	−0.758732	+	1.04430i	−0.284482	−	1.79615i	0.103135	+	0.317418i	0.782181	−	1.07658i	2.09157	+	1.06571i	−1.87718	−	1.87718i	−2.86504	−	0.930908i	−0.292044	+	0.0948907i	0.530812	+	1.63367i
5.14	−0.571426	+	0.786500i	−0.433477	−	2.73687i	0.325979	+	1.00326i	−2.31604	+	3.18776i	2.40025	+	1.22299i	0.174429	+	0.174429i	−2.82451	−	0.917739i	−4.44938	+	1.44569i	−1.18372	−	3.64313i
5.15	−0.530379	+	0.730004i	0.0202181	+	0.127652i	0.366430	+	1.12776i	0.681054	−	0.937390i	−0.103910	−	0.0529446i	1.18395	+	1.18395i	−2.73395	−	0.888316i	2.83728	−	0.921889i	0.323082	+	0.994343i
5.16	−0.514426	+	0.708046i	0.447706	+	2.82670i	0.381338	+	1.17364i	0.849527	−	1.16927i	−2.23175	−	1.13713i	2.17552	+	2.17552i	−2.69188	−	0.874644i	−4.93664	+	1.60401i	0.390881	+	1.20301i
5.17	−0.258843	+	0.356266i	0.168013	+	1.06079i	0.558108	+	1.71768i	−2.15700	+	2.96886i	−0.421413	−	0.214720i	−2.50933	−	2.50933i	−1.59405	−	0.517937i	1.75612	−	0.570599i	−0.499380	−	1.53693i
5.18	−0.242293	+	0.333488i	−0.394082	−	2.48813i	0.565526	+	1.74051i	−0.833669	+	1.14745i	0.925246	+	0.471436i	1.07855	+	1.07855i	−1.50154	−	0.487879i	−3.18234	+	1.03401i	−0.180667	−	0.556037i
5.19	−0.139199	+	0.191591i	−0.339724	−	2.14493i	0.600703	+	1.84877i	2.31959	−	3.19264i	0.458239	+	0.233484i	0.155182	+	0.155182i	−0.888283	−	0.288621i	−1.63216	+	0.530320i	0.288797	+	0.888825i
5.20	−0.0442297	+	0.0608769i	−0.000985846	−	0.00622439i	0.616284	+	1.89673i	−0.771719	+	1.06218i	0.000422525	0	0.000215287i	0.591034	+	0.591034i	−0.285855	−	0.0928800i	2.85313	−	0.927039i	−0.0305294	−	0.0939598i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
451.bp	even	20	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	451.2.bp.a	yes	320
11.c	even	5	1		451.2.bm.a	✓	320
41.g	even	20	1		451.2.bm.a	✓	320
451.bp	even	20	1	inner	451.2.bp.a	yes	320

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
451.2.bm.a	✓	320	11.c	even	5	1
451.2.bm.a	✓	320	41.g	even	20	1
451.2.bp.a	yes	320	1.a	even	1	1	trivial
451.2.bp.a	yes	320	451.bp	even	20	1	inner

Hecke kernels

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