Newform orbit 187.4.e.a

• Label: 187.4.e.a
• Level: $187$
• Weight: $4$
• Character orbit: 187.e
• Analytic conductor: $11.033$
• Analytic rank: $0$
• Dimension: $88$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	187.e (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.0333571711\)
Analytic rank:	\(0\)
Dimension:	\(88\)
Relative dimension:	\(44\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 88 q - 336 q^{4} - 16 q^{5} + 24 q^{6}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
89.1		−	5.48483i	1.46422	−	1.46422i	−22.0834			12.5916	−	12.5916i	−8.03102	−	8.03102i	−9.16616	−	9.16616i			77.2450i			22.7121i	−69.0628	−	69.0628i
89.2		−	5.45854i	−6.26843	+	6.26843i	−21.7956			−6.44895	+	6.44895i	34.2165	+	34.2165i	3.26906	+	3.26906i			75.3041i		−	51.5864i	35.2019	+	35.2019i
89.3		−	5.16290i	2.06487	−	2.06487i	−18.6556			−7.86600	+	7.86600i	−10.6607	−	10.6607i	11.8761	+	11.8761i			55.0138i			18.4726i	40.6114	+	40.6114i
89.4		−	4.82029i	−3.84421	+	3.84421i	−15.2352			10.0087	−	10.0087i	18.5302	+	18.5302i	13.4471	+	13.4471i			34.8760i		−	2.55588i	−48.2451	−	48.2451i
89.5		−	4.73839i	−0.403922	+	0.403922i	−14.4523			−7.30649	+	7.30649i	1.91394	+	1.91394i	−9.69039	−	9.69039i			30.5737i			26.6737i	34.6210	+	34.6210i
89.6		−	4.72637i	5.51714	−	5.51714i	−14.3385			2.25716	−	2.25716i	−26.0760	−	26.0760i	−13.1565	−	13.1565i			29.9583i		−	33.8777i	−10.6682	−	10.6682i
89.7		−	4.31415i	−4.38912	+	4.38912i	−10.6119			6.02814	−	6.02814i	18.9353	+	18.9353i	−18.6215	−	18.6215i			11.2681i		−	11.5287i	−26.0063	−	26.0063i
89.8		−	4.05621i	5.20171	−	5.20171i	−8.45284			10.5563	−	10.5563i	−21.0993	−	21.0993i	17.2879	+	17.2879i			1.83683i		−	27.1157i	−42.8185	−	42.8185i
89.9		−	3.83291i	5.83705	−	5.83705i	−6.69123			−12.2811	+	12.2811i	−22.3729	−	22.3729i	−7.29619	−	7.29619i		−	5.01639i		−	41.1424i	47.0724	+	47.0724i
89.10		−	3.40878i	−4.69894	+	4.69894i	−3.61980			−13.4576	+	13.4576i	16.0177	+	16.0177i	−0.402064	−	0.402064i		−	14.9311i		−	17.1600i	45.8741	+	45.8741i
89.11		−	3.39624i	−4.69047	+	4.69047i	−3.53447			1.19656	−	1.19656i	15.9300	+	15.9300i	4.67024	+	4.67024i		−	15.1660i		−	17.0010i	−4.06380	−	4.06380i
89.12		−	3.04777i	0.933969	−	0.933969i	−1.28890			1.03811	−	1.03811i	−2.84652	−	2.84652i	−18.1869	−	18.1869i		−	20.4539i			25.2554i	−3.16392	−	3.16392i
89.13		−	2.56886i	5.61121	−	5.61121i	1.40096			0.788609	−	0.788609i	−14.4144	−	14.4144i	10.4144	+	10.4144i		−	24.1497i		−	35.9713i	−2.02582	−	2.02582i
89.14		−	2.43484i	2.27412	−	2.27412i	2.07155			11.4454	−	11.4454i	−5.53712	−	5.53712i	−11.6580	−	11.6580i		−	24.5226i			16.6567i	−27.8676	−	27.8676i
89.15		−	2.23546i	0.387877	−	0.387877i	3.00270			−10.6065	+	10.6065i	−0.867085	−	0.867085i	−6.26544	−	6.26544i		−	24.5961i			26.6991i	23.7104	+	23.7104i
89.16		−	1.84506i	−3.06226	+	3.06226i	4.59574			15.1814	−	15.1814i	5.65006	+	5.65006i	3.21730	+	3.21730i		−	23.2399i			8.24517i	−28.0107	−	28.0107i
89.17		−	1.77741i	3.77671	−	3.77671i	4.84083			−11.6466	+	11.6466i	−6.71275	−	6.71275i	20.6826	+	20.6826i		−	22.8234i		−	1.52712i	20.7008	+	20.7008i
89.18		−	1.65075i	−0.0235324	+	0.0235324i	5.27501			−1.08325	+	1.08325i	0.0388462	+	0.0388462i	6.86151	+	6.86151i		−	21.9138i			26.9989i	1.78818	+	1.78818i
89.19		−	1.56698i	−6.90512	+	6.90512i	5.54456			1.28961	−	1.28961i	10.8202	+	10.8202i	22.2332	+	22.2332i		−	21.2241i		−	68.3614i	−2.02080	−	2.02080i
89.20		−	1.42625i	−6.15084	+	6.15084i	5.96581			−4.26112	+	4.26112i	8.77263	+	8.77263i	−19.2402	−	19.2402i		−	19.9187i		−	48.6658i	6.07742	+	6.07742i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
17.c	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	187.4.e.a	✓	88
17.c	even	4	1	inner	187.4.e.a	✓	88

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
187.4.e.a	✓	88	1.a	even	1	1	trivial
187.4.e.a	✓	88	17.c	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(187, [\chi])\).