Newform orbit 101.4.e.a

• Label: 101.4.e.a
• Level: $101$
• Weight: $4$
• Character orbit: 101.e
• Analytic conductor: $5.959$
• Analytic rank: $0$
• Dimension: $96$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 101 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	101.e (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.95919291058\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(24\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q - 5 q^{2} - 5 q^{3} + 85 q^{4} + q^{5} - 14 q^{6} - 5 q^{7} - 5 q^{8} + 219 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
6.1	−3.19684	+	4.40008i	2.05029	+	2.82199i	−6.66874	−	20.5243i	−11.3652	+	8.25730i	−18.9714			−5.61967	−	7.73481i	70.2464	+	22.8244i	4.58355	−	14.1067i		−	76.4051i
6.2	−2.99560	+	4.12309i	−4.49544	−	6.18744i	−5.55413	−	17.0939i	3.04752	−	2.21415i	38.9780			−1.07284	−	1.47664i	48.3417	+	15.7072i	−9.73201	+	29.9521i			19.1979i
6.3	−2.84669	+	3.91813i	1.58704	+	2.18437i	−4.77596	−	14.6989i	10.8594	−	7.88985i	−13.0764			13.6265	+	18.7553i	34.3396	+	11.1576i	6.09068	−	18.7452i			65.0086i
6.4	−2.27413	+	3.13007i	−3.19324	−	4.39512i	−2.15355	−	6.62794i	−9.14883	+	6.64702i	21.0189			−6.12996	−	8.43717i	−3.79360	−	1.23261i	−0.776817	+	2.39080i		−	43.7527i
6.5	−2.21202	+	3.04458i	5.73019	+	7.88692i	−1.90432	−	5.86090i	0.243356	−	0.176809i	−36.6877			0.598825	+	0.824212i	−6.57660	−	2.13687i	−21.0251	+	64.7086i			1.13202i
6.6	−2.17833	+	2.99822i	1.13935	+	1.56818i	−1.77205	−	5.45380i	8.76930	−	6.37127i	−7.18366			−16.7661	−	23.0765i	−7.98515	−	2.59453i	7.18238	−	22.1051i			40.1710i
6.7	−1.90253	+	2.61861i	−2.15754	−	2.96959i	−0.765363	−	2.35554i	−5.97088	+	4.33810i	11.8810			21.6118	+	29.7460i	−17.0025	−	5.52445i	4.17994	−	12.8645i		−	23.8888i
6.8	−1.29822	+	1.78685i	2.22748	+	3.06587i	0.964689	+	2.96901i	−13.3153	+	9.67416i	−8.37000			−1.66006	−	2.28488i	−23.3621	−	7.59079i	3.90560	−	12.0202i		−	36.3517i
6.9	−1.13587	+	1.56339i	−5.41655	−	7.45524i	1.31815	+	4.05685i	11.3053	−	8.21378i	17.8079			−3.69975	−	5.09227i	−22.5427	−	7.32455i	−17.8981	+	55.0847i			27.0043i
6.10	−0.989427	+	1.36183i	−1.38342	−	1.90412i	1.59652	+	4.91359i	10.3170	−	7.49574i	3.96188			1.89890	+	2.61361i	−21.0785	−	6.84883i	6.63165	−	20.4101i			21.4665i
6.11	−0.537282	+	0.739505i	3.02933	+	4.16952i	2.21394	+	6.81381i	7.38493	−	5.36546i	−4.71099			11.0057	+	15.1481i	−13.1831	−	4.28344i	0.135420	−	0.416781i			8.34396i
6.12	0.0438041	−	0.0602912i	−1.80438	−	2.48351i	2.47042	+	7.60317i	−6.72519	+	4.88614i	−0.228773			−15.1283	−	20.8223i	1.13363	+	0.368339i	5.43141	−	16.7162i			0.619503i
6.13	0.0477515	−	0.0657243i	3.68123	+	5.06678i	2.47010	+	7.60218i	−2.33801	+	1.69867i	0.508795			4.77575	+	6.57326i	1.23571	+	0.401506i	−3.77732	+	11.6254i			0.234778i
6.14	0.473285	−	0.651420i	−4.49715	−	6.18980i	2.27179	+	6.99184i	−7.24775	+	5.26580i	−6.16059			9.51114	+	13.0910i	11.7561	+	3.81980i	−9.74578	+	29.9944i			7.21355i
6.15	0.805789	−	1.10907i	4.65688	+	6.40965i	1.89139	+	5.82109i	15.9361	−	11.5783i	10.8612			−13.6360	−	18.7684i	18.4104	+	5.98191i	−11.0536	+	34.0194i		−	27.0040i
6.16	1.29022	−	1.77584i	−0.244166	−	0.336065i	0.983211	+	3.02601i	5.57692	−	4.05187i	−0.911825			−7.88929	−	10.8587i	23.3432	+	7.58467i	8.29014	−	25.5144i		−	15.1315i
6.17	1.48361	−	2.04202i	5.14999	+	7.08835i	0.503403	+	1.54931i	−15.3376	+	11.1434i	22.1151			−14.3661	−	19.7733i	23.1149	+	7.51048i	−15.3789	+	47.3313i			47.8523i
6.18	1.55954	−	2.14653i	−2.19364	−	3.01929i	0.296729	+	0.913239i	15.1925	−	11.0380i	−9.90207			11.8963	+	16.3738i	22.6102	+	7.34651i	4.03942	−	12.4321i		−	49.8255i
6.19	1.69210	−	2.32898i	1.30623	+	1.79788i	−0.0887978	−	0.273291i	−8.07994	+	5.87042i	6.39750			15.1830	+	20.8976i	21.1163	+	6.86110i	6.81734	−	20.9816i			28.7514i
6.20	2.18599	−	3.00875i	−5.24689	−	7.22172i	−1.80191	−	5.54572i	4.82174	−	3.50320i	−33.1980			−11.1287	−	15.3174i	7.67133	+	2.49257i	−16.2800	+	50.1046i		−	22.1653i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
101.e	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	101.4.e.a	✓	96
101.e	even	10	1	inner	101.4.e.a	✓	96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
101.4.e.a	✓	96	1.a	even	1	1	trivial
101.4.e.a	✓	96	101.e	even	10	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(101, [\chi])\).