Newform orbit 128.3.l.a

• Label: 128.3.l.a
• Level: $128$
• Weight: $3$
• Character orbit: 128.l
• Analytic conductor: $3.488$
• Analytic rank: $0$
• Dimension: $496$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.l (of order \(32\), degree \(16\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.48774738381\)
Analytic rank:	\(0\)
Dimension:	\(496\)
Relative dimension:	\(31\) over \(\Q(\zeta_{32})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−1.99185	−	0.180370i	1.05127	−	0.862751i	3.93493	+	0.718539i	−7.90123	−	2.39681i	−2.24958	+	1.52885i	1.29801	+	6.52556i	−7.70819	−	2.14097i	−1.39499	+	7.01311i	15.3057	+	6.19923i
3.2	−1.98170	−	0.269964i	−2.40785	+	1.97607i	3.85424	+	1.06997i	4.69198	+	1.42330i	5.30509	−	3.26594i	−0.744763	−	3.74418i	−7.34908	−	3.16086i	0.137064	−	0.689066i	−8.91384	−	4.08721i
3.3	−1.90117	+	0.620914i	0.779996	−	0.640126i	3.22893	−	2.36093i	0.179045	+	0.0543127i	−1.08545	+	1.70130i	−2.44195	−	12.2765i	−4.67283	+	6.49343i	−1.55718	+	7.82847i	−0.374119	+	0.00791361i
3.4	−1.84253	−	0.777866i	1.79949	−	1.47680i	2.78985	+	2.86649i	5.80468	+	1.76083i	−4.46437	+	1.32129i	0.867168	+	4.35955i	−2.91064	−	7.45172i	−0.698600	+	3.51210i	−9.32562	−	7.75965i
3.5	−1.78050	+	0.910937i	3.84622	−	3.15651i	2.34039	−	3.24385i	4.46942	+	1.35578i	−3.97282	+	9.12384i	1.40191	+	7.04787i	−1.21212	+	7.90764i	3.07403	−	15.4542i	−9.19284	+	1.65738i
3.6	−1.77728	+	0.917214i	−4.35347	+	3.57280i	2.31744	−	3.26029i	−6.55995	−	1.98994i	4.46031	−	10.3429i	−0.342193	−	1.72032i	−1.12835	+	7.92003i	4.43199	−	22.2811i	13.4841	−	2.48020i
3.7	−1.57051	−	1.23834i	−3.06977	+	2.51930i	0.933028	+	3.88966i	−2.31969	−	0.703669i	7.94087	−	0.155169i	0.668264	+	3.35959i	3.35139	−	7.26417i	1.32084	−	6.64029i	2.77172	+	3.97768i
3.8	−1.52087	−	1.29883i	3.39289	−	2.78447i	0.626076	+	3.95070i	−2.17916	−	0.661042i	−8.77669	−	0.171976i	−1.02400	−	5.14798i	4.17911	−	6.82166i	2.00260	−	10.0677i	2.45564	+	3.83572i
3.9	−1.39308	+	1.43504i	0.447688	−	0.367408i	−0.118660	−	3.99824i	−2.47385	−	0.750435i	−0.0964209	+	1.15428i	0.987061	+	4.96229i	5.90292	+	5.39958i	−1.69038	+	8.49810i	4.52318	−	2.50465i
3.10	−1.31385	+	1.50791i	−2.45029	+	2.01090i	−0.547604	−	3.96234i	9.14318	+	2.77355i	0.187046	−	6.33684i	0.716485	+	3.60202i	6.69433	+	4.38017i	0.204383	−	1.02750i	−16.1950	+	10.1431i
3.11	−0.849476	−	1.81063i	−0.740915	+	0.608053i	−2.55678	+	3.07618i	−2.60449	−	0.790064i	1.73035	+	0.824998i	−0.481425	−	2.42029i	7.74175	+	2.01625i	−1.57659	+	7.92604i	0.781937	+	5.38692i
3.12	−0.687532	+	1.87811i	3.91403	−	3.21216i	−3.05460	−	2.58252i	−8.46864	−	2.56894i	3.34178	+	9.55944i	−0.593205	−	2.98225i	6.95040	−	3.96131i	3.24584	−	16.3179i	10.6472	−	14.1388i
3.13	−0.630182	+	1.89812i	−2.02704	+	1.66355i	−3.20574	−	2.39233i	−2.42484	−	0.735568i	−1.88021	−	4.89591i	−0.539873	−	2.71413i	6.56113	−	4.57729i	−0.414318	+	2.08292i	2.92429	−	4.13911i
3.14	−0.494075	−	1.93801i	0.211016	−	0.173176i	−3.51178	+	1.91505i	7.43419	+	2.25514i	−0.439875	−	0.323389i	2.23153	+	11.2187i	5.44647	+	5.85969i	−1.74128	+	8.75398i	0.697434	−	15.5218i
3.15	−0.203195	+	1.98965i	2.70039	−	2.21615i	−3.91742	−	0.808573i	7.86468	+	2.38573i	3.86067	+	5.82314i	−2.00235	−	10.0665i	2.40478	−	7.63001i	0.624959	−	3.14188i	−6.34482	+	15.1632i
3.16	−0.0383871	−	1.99963i	−4.01639	+	3.29616i	−3.99705	+	0.153520i	6.07117	+	1.84167i	6.74529	+	7.90476i	−2.47965	−	12.4660i	0.460419	+	7.98674i	3.51086	−	17.6503i	3.44961	−	12.2108i
3.17	0.0173622	−	1.99992i	3.90317	−	3.20325i	−3.99940	−	0.0694462i	4.26052	+	1.29242i	−6.33848	−	7.86165i	−0.713727	−	3.58815i	−0.208325	+	7.99729i	3.21811	−	16.1785i	2.65871	−	8.49828i
3.18	0.286149	+	1.97942i	0.798268	−	0.655122i	−3.83624	+	1.13282i	0.972729	+	0.295074i	1.52519	+	1.39265i	1.76467	+	8.87160i	−3.34006	−	7.26939i	−1.54777	+	7.78114i	−0.305732	+	2.00988i
3.19	0.359443	−	1.96744i	1.06123	−	0.870929i	−3.74160	−	1.41436i	−6.51407	−	1.97602i	−1.33205	−	2.40095i	−0.702367	−	3.53104i	−4.12755	+	6.85298i	−1.38812	+	6.97855i	−6.22913	+	12.1057i
3.20	0.768183	+	1.84659i	−4.58227	+	3.76057i	−2.81979	+	2.83704i	2.93176	+	0.889341i	−10.4642	−	5.57276i	1.62220	+	8.15533i	−7.40496	−	3.02764i	5.09947	−	25.6368i	0.609882	+	6.09694i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
128.l	odd	32	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	128.3.l.a	✓	496
128.l	odd	32	1	inner	128.3.l.a	✓	496

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
128.3.l.a	✓	496	1.a	even	1	1	trivial
128.3.l.a	✓	496	128.l	odd	32	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(128, [\chi])\).