Newform orbit 805.2.v.a

• Label: 805.2.v.a
• Level: $805$
• Weight: $2$
• Character orbit: 805.v
• Analytic conductor: $6.428$
• Analytic rank: $0$
• Dimension: $352$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.v (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.42795736271\)
Analytic rank:	\(0\)
Dimension:	\(352\)
Relative dimension:	\(88\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 352 q + 8 q^{7} - 24 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
47.1	−2.68889	+	0.720486i	−0.293810	+	1.09651i	4.97897	−	2.87461i	−2.04040	+	0.914756i		−	3.16009i	−2.40464	−	1.10349i	−7.37998	+	7.37998i	1.48206	+	0.855668i	4.82733	−	3.92975i
47.2	−2.67737	+	0.717398i	0.756633	−	2.82379i	4.92159	−	2.84148i	2.23550	−	0.0503084i			8.10314i	1.61435	+	2.09615i	−7.21848	+	7.21848i	−4.80325	−	2.77316i	−5.94917	+	1.73844i
47.3	−2.62719	+	0.703954i	−0.767006	+	2.86251i	4.67453	−	2.69884i	0.734804	−	2.11189i		−	8.06029i	1.58924	−	2.11526i	−6.53456	+	6.53456i	−5.00757	−	2.89112i	−0.443800	+	6.06560i
47.4	−2.56835	+	0.688188i	0.110411	−	0.412060i	4.39079	−	2.53502i	−1.13498	+	1.92661i			1.13430i	2.64308	−	0.118863i	−5.77219	+	5.77219i	2.44047	+	1.40901i	1.58916	−	5.72929i
47.5	−2.51788	+	0.674664i	−0.600216	+	2.24004i	4.15250	−	2.39744i	1.28658	+	1.82885i		−	6.04509i	−0.156826	+	2.64110i	−5.15158	+	5.15158i	−2.05943	−	1.18901i	−4.47332	−	3.73682i
47.6	−2.50973	+	0.672481i	0.491857	−	1.83563i	4.11447	−	2.37549i	0.106506	−	2.23353i			4.93771i	−0.536677	−	2.59075i	−5.05425	+	5.05425i	−0.529553	−	0.305738i	1.23470	+	5.67719i
47.7	−2.37477	+	0.636318i	0.0981369	−	0.366252i	3.50259	−	2.02222i	1.26813	−	1.84169i			0.932211i	−1.88442	+	1.85714i	−3.55416	+	3.55416i	2.47357	+	1.42811i	−1.83962	+	5.18054i
47.8	−2.35542	+	0.631134i	−0.0147650	+	0.0551037i	3.41765	−	1.97318i	2.11130	+	0.736492i		−	0.139111i	−2.51408	−	0.824266i	−3.35609	+	3.35609i	2.59526	+	1.49837i	−5.43783	−	0.402239i
47.9	−2.33603	+	0.625938i	−0.390289	+	1.45658i	3.33320	−	1.92442i	−1.06345	−	1.96700i		−	3.64691i	0.0339333	+	2.64553i	−3.16170	+	3.16170i	0.628777	+	0.363025i	3.71546	+	3.92932i
47.10	−2.32810	+	0.623811i	0.634729	−	2.36884i	3.29884	−	1.90458i	−2.23181	+	0.137855i			5.91084i	−0.352076	+	2.62222i	−3.08334	+	3.08334i	−2.61046	−	1.50715i	5.10988	−	1.71317i
47.11	−2.20548	+	0.590957i	0.224632	−	0.838337i	2.78286	−	1.60669i	−1.60444	−	1.55749i			1.98168i	2.48243	−	0.915160i	−1.95902	+	1.95902i	1.94573	+	1.12337i	4.45896	+	2.48687i
47.12	−2.18268	+	0.584847i	0.650517	−	2.42776i	2.68999	−	1.55307i	−0.0572951	+	2.23533i			5.67948i	−2.53272	−	0.765075i	−1.76742	+	1.76742i	−2.87278	−	1.65860i	−1.18227	−	4.91253i
47.13	−2.07570	+	0.556183i	0.220463	−	0.822777i	2.26716	−	1.30894i	0.741398	+	2.10958i			1.83046i	2.23183	+	1.42090i	−0.938895	+	0.938895i	1.96972	+	1.13722i	−2.71224	−	3.96651i
47.14	−2.06447	+	0.553174i	−0.563135	+	2.10165i	2.22400	−	1.28403i	−2.11828	−	0.716157i		−	4.65032i	2.09617	−	1.61434i	−0.858508	+	0.858508i	−1.50173	−	0.867027i	4.76930	+	0.306708i
47.15	−1.91871	+	0.514118i	−0.890572	+	3.32366i	1.68510	−	0.972891i	−2.15856	+	0.583641i		−	6.83501i	−2.50246	+	0.858893i	0.0761536	−	0.0761536i	−7.65552	−	4.41992i	3.84159	−	2.22959i
47.16	−1.88834	+	0.505979i	−0.751808	+	2.80578i	1.57776	−	0.910921i	2.04967	−	0.893783i		−	5.67867i	−2.50884	−	0.840077i	0.246279	−	0.246279i	−4.70914	−	2.71882i	−3.41824	+	2.72486i
47.17	−1.86138	+	0.498754i	0.652606	−	2.43556i	1.48392	−	0.856739i	2.17445	+	0.521301i			4.85898i	1.61225	−	2.09777i	0.390420	−	0.390420i	−2.90798	−	1.67892i	−4.30748	+	0.114181i
47.18	−1.80837	+	0.484552i	−0.648797	+	2.42134i	1.30337	−	0.752499i	2.22633	+	0.208507i		−	4.69307i	2.26186	+	1.37258i	0.655294	−	0.655294i	−2.84389	−	1.64192i	−4.12706	+	0.701711i
47.19	−1.79577	+	0.481174i	0.151169	−	0.564171i	1.26120	−	0.728155i	−2.23334	+	0.110377i			1.08586i	−1.65532	−	2.06395i	0.714731	−	0.714731i	2.30264	+	1.32943i	3.95745	−	1.27284i
47.20	−1.69784	+	0.454935i	−0.118398	+	0.441866i	0.943646	−	0.544814i	1.67008	−	1.48689i		−	0.804081i	2.50439	+	0.853254i	1.13151	−	1.13151i	2.41685	+	1.39537i	−2.15909	+	3.28428i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
7.d	odd	6	1	inner
35.k	even	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	805.2.v.a	✓	352
5.c	odd	4	1	inner	805.2.v.a	✓	352
7.d	odd	6	1	inner	805.2.v.a	✓	352
35.k	even	12	1	inner	805.2.v.a	✓	352

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
805.2.v.a	✓	352	1.a	even	1	1	trivial
805.2.v.a	✓	352	5.c	odd	4	1	inner
805.2.v.a	✓	352	7.d	odd	6	1	inner
805.2.v.a	✓	352	35.k	even	12	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(805, [\chi])\).