Newform orbit 96.5.m.a

• Label: 96.5.m.a
• Level: $96$
• Weight: $5$
• Character orbit: 96.m
• Analytic conductor: $9.924$
• Analytic rank: $0$
• Dimension: $128$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	96.m (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.92351645605\)
Analytic rank:	\(0\)
Dimension:	\(128\)
Relative dimension:	\(32\) over \(\Q(\zeta_{8})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 128 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−3.91885	+	0.801613i	−4.80062	−	1.98848i	14.7148	−	6.28281i	38.9984	−	16.1536i	20.4069	+	3.94433i	−11.3718	−	11.3718i	−52.6289	+	36.4170i	19.0919	+	19.0919i	−139.880	+	94.5654i
19.2	−3.91387	−	0.825614i	4.80062	+	1.98848i	14.6367	+	6.46269i	41.0395	−	16.9991i	−17.1473	−	11.7461i	39.8685	+	39.8685i	−51.9505	−	37.3784i	19.0919	+	19.0919i	−174.658	+	32.6495i
19.3	−3.90221	+	0.879058i	4.80062	+	1.98848i	14.4545	−	6.86054i	−12.4195	+	5.14434i	−20.4810	−	3.53946i	12.0541	+	12.0541i	−50.3738	+	39.4776i	19.0919	+	19.0919i	43.9415	−	30.9918i
19.4	−3.89979	+	0.889719i	−4.80062	−	1.98848i	14.4168	−	6.93944i	−36.4194	+	15.0854i	20.4906	+	3.48347i	28.3955	+	28.3955i	−50.0484	+	39.8893i	19.0919	+	19.0919i	128.606	−	91.2329i
19.5	−3.77443	−	1.32427i	−4.80062	−	1.98848i	12.4926	+	9.99675i	3.08230	−	1.27673i	15.4863	+	13.8627i	−11.9417	−	11.9417i	−33.9140	−	54.2756i	19.0919	+	19.0919i	−13.3247	+	0.737118i
19.6	−3.60899	−	1.72488i	4.80062	+	1.98848i	10.0496	+	12.4501i	1.41390	−	0.585655i	−13.8955	−	15.4569i	−39.7285	−	39.7285i	−14.7939	−	62.2667i	19.0919	+	19.0919i	−6.11292	−	0.325176i
19.7	−2.80122	+	2.85538i	−4.80062	−	1.98848i	−0.306365	−	15.9971i	−3.83450	+	1.58830i	19.1254	−	8.13741i	−40.6057	−	40.6057i	46.5359	+	43.9365i	19.0919	+	19.0919i	6.20607	−	15.3981i
19.8	−2.43406	+	3.17417i	4.80062	+	1.98848i	−4.15072	−	15.4522i	−37.8877	+	15.6936i	−17.9968	+	10.3979i	−16.3741	−	16.3741i	59.1511	+	24.4366i	19.0919	+	19.0919i	42.4068	−	158.461i
19.9	−2.43211	−	3.17566i	−4.80062	−	1.98848i	−4.16964	+	15.4471i	−45.0019	+	18.6404i	5.36091	+	20.0814i	−57.2930	−	57.2930i	59.1959	−	24.3278i	19.0919	+	19.0919i	168.646	+	97.5753i
19.10	−2.12024	−	3.39184i	4.80062	+	1.98848i	−7.00918	+	14.3830i	−2.50651	+	1.03823i	−3.43384	−	20.4990i	−15.1406	−	15.1406i	63.6461	−	6.72143i	19.0919	+	19.0919i	8.83592	+	6.30039i
19.11	−1.83362	+	3.55497i	−4.80062	−	1.98848i	−9.27568	−	13.0369i	5.98812	−	2.48036i	15.8715	−	13.4200i	50.8637	+	50.8637i	63.3540	−	9.07002i	19.0919	+	19.0919i	−2.16232	+	25.8357i
19.12	−1.65353	−	3.64223i	−4.80062	−	1.98848i	−10.5317	+	12.0451i	13.5792	−	5.62468i	0.695457	+	20.7730i	25.2032	+	25.2032i	61.2854	+	18.4419i	19.0919	+	19.0919i	−42.9399	−	40.1579i
19.13	−0.981308	+	3.87776i	4.80062	+	1.98848i	−14.0741	−	7.61056i	22.0087	−	9.11631i	−12.4217	+	16.6643i	10.8040	+	10.8040i	43.3229	−	47.1076i	19.0919	+	19.0919i	13.7536	+	94.2905i
19.14	−0.532306	−	3.96442i	4.80062	+	1.98848i	−15.4333	+	4.22058i	−22.7160	+	9.40928i	5.32778	−	20.0902i	0.779343	+	0.779343i	24.9474	+	58.9375i	19.0919	+	19.0919i	49.3943	+	85.0473i
19.15	0.0840734	−	3.99912i	4.80062	+	1.98848i	−15.9859	−	0.672439i	28.4020	−	11.7645i	8.35577	−	19.0311i	67.3311	+	67.3311i	−4.03315	+	63.8728i	19.0919	+	19.0919i	−44.6598	−	114.572i
19.16	0.200031	+	3.99500i	−4.80062	−	1.98848i	−15.9200	+	1.59824i	−18.9195	+	7.83673i	6.98370	−	19.5762i	−4.26517	−	4.26517i	−9.56945	−	63.2805i	19.0919	+	19.0919i	−35.0922	−	74.0159i
19.17	0.621102	−	3.95148i	−4.80062	−	1.98848i	−15.2285	−	4.90855i	16.5981	−	6.87516i	−10.8391	+	17.7345i	−43.9321	−	43.9321i	−28.8545	+	57.1263i	19.0919	+	19.0919i	−16.8580	−	69.8573i
19.18	0.638317	+	3.94874i	4.80062	+	1.98848i	−15.1851	+	5.04110i	−18.0299	+	7.46824i	−4.78768	+	20.2257i	60.4929	+	60.4929i	−29.5989	−	56.7442i	19.0919	+	19.0919i	−40.9989	−	66.4284i
19.19	1.31848	+	3.77646i	4.80062	+	1.98848i	−12.5232	+	9.95834i	−12.7536	+	5.28269i	−1.17990	+	20.7511i	−68.8629	−	68.8629i	−54.1188	−	34.1636i	19.0919	+	19.0919i	−36.7651	−	41.1981i
19.20	1.37965	−	3.75454i	4.80062	+	1.98848i	−12.1931	−	10.3599i	21.8774	−	9.06192i	14.0890	−	15.2807i	−43.9499	−	43.9499i	−55.7190	+	31.4865i	19.0919	+	19.0919i	−3.84012	−	94.6419i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
32.h	odd	8	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	96.5.m.a	✓	128
32.h	odd	8	1	inner	96.5.m.a	✓	128

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
96.5.m.a	✓	128	1.a	even	1	1	trivial
96.5.m.a	✓	128	32.h	odd	8	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(96, [\chi])\).