Newform orbit 880.2.v.a

• Label: 880.2.v.a
• Level: $880$
• Weight: $2$
• Character orbit: 880.v
• Analytic conductor: $7.027$
• Analytic rank: $0$
• Dimension: $192$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.v (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.02683537787\)
Analytic rank:	\(0\)
Dimension:	\(192\)
Relative dimension:	\(96\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 192 q - 8 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
131.1	−1.41345	+	0.0465912i	0.0362830	−	0.0362830i	1.99566	−	0.131708i	−0.707107	+	0.707107i	−0.0495936	+	0.0529745i		−	3.47250i	−2.81462	+	0.279142i			2.99737i	0.966512	−	1.03240i
131.2	−1.41005	−	0.108379i	2.41753	−	2.41753i	1.97651	+	0.305642i	−0.707107	+	0.707107i	−3.67085	+	3.14683i		−	2.61905i	−2.75386	−	0.645185i		−	8.68886i	1.07369	−	0.920423i
131.3	−1.40891	−	0.122339i	1.85786	−	1.85786i	1.97007	+	0.344729i	0.707107	−	0.707107i	−2.84485	+	2.39027i		−	1.91467i	−2.73348	−	0.726708i		−	3.90330i	−1.08276	+	0.909745i
131.4	−1.40584	+	0.153626i	0.972252	−	0.972252i	1.95280	−	0.431947i	0.707107	−	0.707107i	−1.21747	+	1.51620i			2.33403i	−2.67897	+	0.907250i			1.10945i	−0.885453	+	1.10271i
131.5	−1.40035	+	0.197521i	−2.28008	+	2.28008i	1.92197	−	0.553198i	−0.707107	+	0.707107i	2.74255	−	3.64327i			2.96928i	−2.58217	+	1.15430i		−	7.39749i	0.850530	−	1.12987i
131.6	−1.40022	−	0.198471i	−1.30588	+	1.30588i	1.92122	+	0.555804i	−0.707107	+	0.707107i	2.08769	−	1.56933i			0.581174i	−2.57981	−	1.15955i		−	0.410632i	1.13044	−	0.849763i
131.7	−1.39781	−	0.214755i	−0.808629	+	0.808629i	1.90776	+	0.600375i	0.707107	−	0.707107i	1.30397	−	0.956654i			4.43965i	−2.53776	−	1.24891i			1.69224i	−1.14026	+	0.836548i
131.8	−1.39170	+	0.251354i	−0.521376	+	0.521376i	1.87364	−	0.699617i	0.707107	−	0.707107i	0.594547	−	0.856647i		−	3.98918i	−2.43169	+	1.44460i			2.45633i	−0.806344	+	1.16181i
131.9	−1.34893	+	0.424727i	0.963076	−	0.963076i	1.63921	−	1.14585i	−0.707107	+	0.707107i	−0.890075	+	1.70816i		−	2.95448i	−1.72451	+	2.24189i			1.14497i	0.653509	−	1.25416i
131.10	−1.33742	−	0.459670i	−1.51302	+	1.51302i	1.57741	+	1.22955i	0.707107	−	0.707107i	2.71904	−	1.32806i			0.385479i	−1.54448	−	2.36951i		−	1.57845i	−1.27074	+	0.620666i
131.11	−1.31319	−	0.524921i	0.556939	−	0.556939i	1.44892	+	1.37864i	0.707107	−	0.707107i	−1.02371	+	0.439016i		−	0.993498i	−1.17902	−	2.57097i			2.37964i	−1.29974	+	0.557388i
131.12	−1.30641	+	0.541574i	−1.95240	+	1.95240i	1.41339	−	1.41503i	0.707107	−	0.707107i	1.49326	−	3.60799i		−	1.49985i	−1.08012	+	2.61406i		−	4.62371i	−0.540818	+	1.30672i
131.13	−1.29385	−	0.570911i	1.55695	−	1.55695i	1.34812	+	1.47735i	−0.707107	+	0.707107i	−2.90336	+	1.12559i			3.28741i	−0.900837	−	2.68114i		−	1.84822i	1.31859	−	0.511199i
131.14	−1.27713	+	0.607401i	0.106504	−	0.106504i	1.26213	−	1.55146i	0.707107	−	0.707107i	−0.0713286	+	0.200709i			1.34164i	−0.669543	+	2.74804i			2.97731i	−0.473571	+	1.33257i
131.15	−1.24765	−	0.665865i	1.00128	−	1.00128i	1.11325	+	1.66153i	−0.707107	+	0.707107i	−1.91596	+	0.582527i		−	1.56480i	−0.282583	−	2.81428i			0.994873i	1.35306	−	0.411382i
131.16	−1.22839	+	0.700747i	−0.786273	+	0.786273i	1.01791	−	1.72159i	−0.707107	+	0.707107i	0.414875	−	1.51683i			3.29658i	−0.0439927	+	2.82808i			1.76355i	0.373103	−	1.36411i
131.17	−1.22016	−	0.714993i	−1.75153	+	1.75153i	0.977571	+	1.74481i	−0.707107	+	0.707107i	3.38947	−	0.884812i		−	5.25894i	0.0547349	−	2.82790i		−	3.13571i	1.36836	−	0.357206i
131.18	−1.21230	+	0.728236i	1.80591	−	1.80591i	0.939345	−	1.76568i	−0.707107	+	0.707107i	−0.874177	+	3.50444i			0.403519i	0.147064	+	2.82460i		−	3.52263i	0.342285	−	1.37217i
131.19	−1.19532	+	0.755788i	−0.569194	+	0.569194i	0.857569	−	1.80681i	−0.707107	+	0.707107i	0.250178	−	1.11056i		−	0.942779i	0.340500	+	2.80786i			2.35204i	0.310795	−	1.37964i
131.20	−1.11184	+	0.873966i	1.96083	−	1.96083i	0.472367	−	1.94342i	0.707107	−	0.707107i	−0.466427	+	3.89383i			0.475480i	1.17328	+	2.57360i		−	4.68973i	−0.168201	+	1.40418i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.b	odd	2	1	inner
16.f	odd	4	1	inner
176.i	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	880.2.v.a	✓	192
11.b	odd	2	1	inner	880.2.v.a	✓	192
16.f	odd	4	1	inner	880.2.v.a	✓	192
176.i	even	4	1	inner	880.2.v.a	✓	192

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
880.2.v.a	✓	192	1.a	even	1	1	trivial
880.2.v.a	✓	192	11.b	odd	2	1	inner
880.2.v.a	✓	192	16.f	odd	4	1	inner
880.2.v.a	✓	192	176.i	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(880, [\chi])\).