Newform orbit 456.2.v.a

• Label: 456.2.v.a
• Level: $456$
• Weight: $2$
• Character orbit: 456.v
• Analytic conductor: $3.641$
• Analytic rank: $0$
• Dimension: $152$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.v (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.64117833217\)
Analytic rank:	\(0\)
Dimension:	\(152\)
Relative dimension:	\(76\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 152 q - 4 q^{4} - 5 q^{6} - 16 q^{7} - 2 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
221.1	−1.41419	+	0.00738262i	−1.73120	+	0.0542406i	1.99989	−	0.0208809i	1.37169	+	2.37583i	2.44785	−	0.0894876i	−3.31665			−2.82808	+	0.0442941i	2.99412	−	0.187803i	−1.95737	−	3.34976i
221.2	−1.41271	+	0.0652192i	0.389136	+	1.68777i	1.99149	−	0.184271i	0.620253	+	1.07431i	−0.659812	−	2.35895i	−1.16667			−2.80138	+	0.390205i	−2.69715	+	1.31355i	−0.946302	−	1.47723i
221.3	−1.39336	−	0.241988i	−1.66328	−	0.483207i	1.88288	+	0.674352i	−1.26700	−	2.19451i	2.20062	+	1.07577i	2.42976			−2.46034	−	1.39525i	2.53302	+	1.60742i	1.23434	+	3.36433i
221.4	−1.38409	+	0.290316i	1.70720	−	0.292340i	1.83143	−	0.803649i	−0.458427	−	0.794019i	−2.27806	+	0.900254i	2.82659			−2.30156	+	1.64402i	2.82907	−	0.998167i	0.865023	+	0.965909i
221.5	−1.37583	−	0.327255i	1.44592	+	0.953578i	1.78581	+	0.900492i	−1.05313	−	1.82407i	−1.67728	−	1.78514i	−1.57938			−2.16228	−	1.82334i	1.18138	+	2.75760i	0.851986	+	2.85424i
221.6	−1.35988	+	0.388219i	−0.424820	−	1.67915i	1.69857	−	1.05587i	−1.86413	−	3.22878i	1.22958	+	2.11852i	−1.25457			−1.89995	+	2.09527i	−2.63906	+	1.42667i	3.78848	+	3.66707i
221.7	−1.35418	+	0.407678i	0.592993	−	1.62738i	1.66760	−	1.10414i	0.762671	+	1.32099i	−0.139572	+	2.44551i	−3.74205			−1.80809	+	2.17504i	−2.29672	−	1.93005i	−1.57133	−	1.47792i
221.8	−1.34544	−	0.435649i	1.37531	−	1.05287i	1.62042	+	1.17228i	2.00962	+	3.48077i	−2.30907	+	0.817422i	1.14367			−1.66947	−	2.28317i	0.782931	−	2.89604i	−1.18743	−	5.55866i
221.9	−1.32913	+	0.483120i	−0.933526	−	1.45895i	1.53319	−	1.28426i	1.49167	+	2.58365i	1.94563	+	1.48813i	3.57235			−1.41736	+	2.44767i	−1.25706	+	2.72393i	−3.23084	−	2.71336i
221.10	−1.32121	−	0.504383i	−1.09570	+	1.34144i	1.49119	+	1.33279i	1.34037	+	2.32159i	2.12424	−	1.21967i	2.69559			−1.29794	−	2.51303i	−0.598899	−	2.93961i	−0.599941	−	3.74337i
221.11	−1.29437	+	0.569751i	−0.837571	+	1.51607i	1.35077	−	1.47493i	−0.869425	−	1.50589i	0.220341	−	2.43956i	−0.953265			−0.908045	+	2.67870i	−1.59695	−	2.53964i	1.98334	+	1.45382i
221.12	−1.28758	−	0.584931i	1.44953	−	0.948077i	1.31571	+	1.50629i	−0.741716	−	1.28469i	−2.42095	+	0.372844i	−4.16740			−0.813006	−	2.70906i	1.20230	−	2.74854i	0.203562	+	2.08799i
221.13	−1.23174	−	0.694852i	−0.790968	−	1.54090i	1.03436	+	1.71175i	0.265769	+	0.460326i	−0.0964313	+	2.44759i	1.29375			−0.0846489	−	2.82716i	−1.74874	+	2.43760i	−0.00750002	−	0.751672i
221.14	−1.14060	+	0.836079i	−1.73174	−	0.0326779i	0.601945	−	1.90727i	−0.869425	−	1.50589i	2.00255	−	1.41060i	−0.953265			0.908045	+	2.67870i	2.99786	+	0.113179i	2.25071	+	0.990711i
221.15	−1.08296	+	0.909503i	0.796723	+	1.53793i	0.345609	−	1.96991i	1.49167	+	2.58365i	−2.26157	−	0.940898i	3.57235			1.41736	+	2.44767i	−1.73046	+	2.45061i	−3.96526	−	1.44131i
221.16	−1.05738	−	0.939125i	1.52807	+	0.815471i	0.236087	+	1.98602i	0.165799	+	0.287172i	−0.849918	−	2.29731i	4.65099			1.61549	−	2.32168i	1.67001	+	2.49220i	0.0943789	−	0.459355i
221.17	−1.03557	−	0.963113i	−1.63644	+	0.567494i	0.144825	+	1.99475i	−0.571119	−	0.989207i	2.24122	+	0.988400i	−0.203302			1.77119	−	2.20519i	2.35590	−	1.85734i	−0.361283	+	1.57445i
221.18	−1.03015	+	0.968914i	1.70585	+	0.300142i	0.122413	−	1.99625i	0.762671	+	1.32099i	−2.04809	+	1.34363i	−3.74205			1.80809	+	2.17504i	2.81983	+	1.02399i	−2.06559	−	0.621849i
221.19	−1.03010	−	0.968966i	−0.332067	+	1.69992i	0.122210	+	1.99626i	−0.489065	−	0.847086i	1.98923	−	1.42933i	−2.59730			1.80842	−	2.17477i	−2.77946	−	1.12898i	−0.317012	+	1.34647i
221.20	−1.02938	−	0.969730i	0.842716	−	1.51322i	0.119248	+	1.99644i	−1.97169	−	3.41506i	−2.33489	+	0.740470i	2.41350			1.81326	−	2.17074i	−1.57966	−	2.55043i	−1.28207	+	5.42740i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
8.b	even	2	1	inner
19.d	odd	6	1	inner
24.h	odd	2	1	inner
57.f	even	6	1	inner
152.l	odd	6	1	inner
456.v	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	456.2.v.a	✓	152
3.b	odd	2	1	inner	456.2.v.a	✓	152
8.b	even	2	1	inner	456.2.v.a	✓	152
19.d	odd	6	1	inner	456.2.v.a	✓	152
24.h	odd	2	1	inner	456.2.v.a	✓	152
57.f	even	6	1	inner	456.2.v.a	✓	152
152.l	odd	6	1	inner	456.2.v.a	✓	152
456.v	even	6	1	inner	456.2.v.a	✓	152

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
456.2.v.a	✓	152	1.a	even	1	1	trivial
456.2.v.a	✓	152	3.b	odd	2	1	inner
456.2.v.a	✓	152	8.b	even	2	1	inner
456.2.v.a	✓	152	19.d	odd	6	1	inner
456.2.v.a	✓	152	24.h	odd	2	1	inner
456.2.v.a	✓	152	57.f	even	6	1	inner
456.2.v.a	✓	152	152.l	odd	6	1	inner
456.2.v.a	✓	152	456.v	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(456, [\chi])\).