Newform orbit 187.3.n.a

• Label: 187.3.n.a
• Level: $187$
• Weight: $3$
• Character orbit: 187.n
• Analytic conductor: $5.095$
• Analytic rank: $0$
• Dimension: $240$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	187.n (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.09538094354\)
Analytic rank:	\(0\)
Dimension:	\(240\)
Relative dimension:	\(30\) over \(\Q(\zeta_{16})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 240 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
12.1	−1.49143	−	3.60062i	−0.159190	+	0.106367i	−7.91169	+	7.91169i	1.83132	+	0.364272i	0.620408	+	0.414543i	8.50387	−	1.69152i	25.8842	+	10.7216i	−3.43012	+	8.28105i	−1.41967	−	7.13716i
12.2	−1.47786	−	3.56787i	−4.12724	+	2.75773i	−7.71719	+	7.71719i	−4.39479	−	0.874178i	15.9387	+	10.6499i	−11.2712	+	2.24198i	24.6674	+	10.2176i	5.98484	−	14.4487i	3.37593	+	16.9719i
12.3	−1.28085	−	3.09225i	3.08325	−	2.06016i	−5.09299	+	5.09299i	−6.64028	−	1.32083i	−10.3197	−	6.89541i	−4.15737	+	0.826952i	9.90315	+	4.10202i	1.81802	−	4.38908i	4.42087	+	22.2252i
12.4	−1.24025	−	2.99422i	3.78151	−	2.52673i	−4.59871	+	4.59871i	2.66317	+	0.529738i	−12.2556	−	8.18892i	8.01810	−	1.59490i	7.49621	+	3.10503i	4.47134	−	10.7948i	−1.71684	−	8.63113i
12.5	−1.11518	−	2.69229i	−0.415168	+	0.277407i	−3.17636	+	3.17636i	−2.77091	−	0.551168i	1.20985	+	0.808394i	0.258599	−	0.0514385i	1.32475	+	0.548728i	−3.34874	+	8.08457i	1.60616	+	8.07474i
12.6	−1.03236	−	2.49233i	−3.70869	+	2.47807i	−2.31752	+	2.31752i	2.45653	+	0.488635i	10.0049	+	6.68503i	6.05988	−	1.20539i	−1.80080	−	0.745914i	4.16941	−	10.0659i	−1.31818	−	6.62694i
12.7	−0.890389	−	2.14959i	−2.96173	+	1.97896i	−0.999515	+	0.999515i	−7.82156	−	1.55580i	6.89104	+	4.60445i	3.41558	−	0.679401i	−5.55985	−	2.30297i	1.41138	−	3.40737i	3.61989	+	18.1984i
12.8	−0.748538	−	1.80713i	3.80497	−	2.54240i	0.123012	−	0.123012i	4.79354	+	0.953495i	−7.44262	−	4.97300i	−3.84064	+	0.763951i	−7.54291	−	3.12437i	4.56985	−	11.0326i	−1.86506	−	9.37629i
12.9	−0.621454	−	1.50032i	1.42125	−	0.949651i	0.963662	−	0.963662i	−4.43671	−	0.882517i	−2.30803	−	1.54217i	−8.52693	+	1.69611i	−8.04597	−	3.33275i	−2.32603	+	5.61553i	1.43315	+	7.20495i
12.10	−0.594116	−	1.43432i	1.45027	−	0.969042i	1.12412	−	1.12412i	4.06483	+	0.808545i	−2.25155	−	1.50444i	12.2241	−	2.43153i	−8.01750	−	3.32096i	−2.27990	+	5.50417i	−1.25527	−	6.31065i
12.11	−0.443603	−	1.07095i	−4.22850	+	2.82539i	1.87827	−	1.87827i	6.05622	+	1.20466i	4.90164	+	3.27517i	−6.08060	+	1.20951i	−7.12856	−	2.95275i	6.45321	−	15.5794i	−1.39643	−	7.02032i
12.12	−0.346540	−	0.836622i	−3.08023	+	2.05814i	2.24858	−	2.24858i	−1.47174	−	0.292747i	2.78931	+	1.86376i	3.43949	−	0.684156i	−6.00693	−	2.48815i	1.80771	−	4.36419i	0.265098	+	1.33274i
12.13	−0.333431	−	0.804974i	2.39985	−	1.60353i	2.29162	−	2.29162i	−8.07136	−	1.60549i	−2.09098	−	1.39715i	12.3363	−	2.45384i	−5.82869	−	2.41432i	−0.256173	+	0.618456i	1.39886	+	7.03256i
12.14	−0.188848	−	0.455918i	−1.13227	+	0.756556i	2.65623	−	2.65623i	−1.54334	−	0.306990i	0.558753	+	0.373347i	−12.4816	+	2.48275i	−3.53632	−	1.46479i	−2.73450	+	6.60167i	0.151494	+	0.761613i
12.15	−0.162153	−	0.391473i	−0.793795	+	0.530397i	2.70147	−	2.70147i	5.81166	+	1.15601i	0.336352	+	0.224743i	3.61839	−	0.719742i	−3.06150	−	1.26811i	−3.09536	+	7.47286i	−0.489833	−	2.46256i
12.16	−0.0845964	−	0.204234i	4.45306	−	2.97544i	2.79387	−	2.79387i	−4.28555	−	0.852449i	−0.984399	−	0.657754i	−3.05146	+	0.606972i	−1.62389	−	0.672637i	7.53236	−	18.1847i	0.188443	+	0.947369i
12.17	0.261269	+	0.630759i	2.18713	−	1.46139i	2.49883	−	2.49883i	6.23133	+	1.23949i	1.49321	+	0.997734i	−2.22505	+	0.442589i	4.75206	+	1.96837i	−0.796293	+	1.92242i	0.846234	+	4.25431i
12.18	0.436334	+	1.05340i	2.74063	−	1.83123i	1.90916	−	1.90916i	−0.702233	−	0.139683i	3.12486	+	2.08796i	−0.134361	+	0.0267261i	7.05775	+	2.92342i	0.713504	−	1.72255i	−0.159266	−	0.800683i
12.19	0.490183	+	1.18341i	−4.84162	+	3.23507i	1.66826	−	1.66826i	−4.32751	−	0.860796i	−6.20168	−	4.14383i	−5.30625	+	1.05548i	7.52560	+	3.11721i	9.53149	−	23.0110i	−1.10260	−	5.54315i
12.20	0.542442	+	1.30957i	−2.33405	+	1.55956i	1.40770	−	1.40770i	−0.733604	−	0.145923i	−3.30844	−	2.21063i	10.8083	−	2.14990i	7.84535	+	3.24965i	−0.428600	+	1.03473i	−0.206841	−	1.03986i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
17.e	odd	16	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	187.3.n.a	✓	240
17.e	odd	16	1	inner	187.3.n.a	✓	240

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
187.3.n.a	✓	240	1.a	even	1	1	trivial
187.3.n.a	✓	240	17.e	odd	16	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(187, [\chi])\).