Embedded newform 187.2.m.a.10.11

• Label: 187.2.m.a.10.11
• Level: $187$
• Weight: $2$
• Character: 187.10
• Analytic conductor: $1.493$
• Analytic rank: $0$
• Dimension: $128$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.m (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.49320251780\)
Analytic rank:	\(0\)
Dimension:	\(128\)
Relative dimension:	\(16\) over \(\Q(\zeta_{16})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			10.11
Character	\(\chi\)	\(=\)	187.10
Dual form			187.2.m.a.131.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.896657 + 0.371407i) q^{2} +(-1.08522 - 0.725122i) q^{3} +(-0.748164 - 0.748164i) q^{4} +(2.89314 - 0.575481i) q^{5} +(-0.703755 - 1.05324i) q^{6} +(-0.0961645 + 0.483452i) q^{7} +(-1.13579 - 2.74203i) q^{8} +(-0.496147 - 1.19780i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).

\(n\)	\(35\)	\(122\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{3}{16}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

(See \(a_n\) instead)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.896657	+	0.371407i	0.634032	+	0.262625i	0.676465	−	0.736475i	\(-0.263511\pi\)
							−0.0424332	+	0.999099i	\(0.513511\pi\)
\(3\)	−1.08522	−	0.725122i	−0.626553	−	0.418649i	0.201351	−	0.979519i	\(-0.435467\pi\)
							−0.827904	+	0.560870i	\(0.810467\pi\)
\(5\)	2.89314	−	0.575481i	1.29385	−	0.257363i	0.500293	−	0.865856i	\(-0.333226\pi\)
							0.793559	+	0.608493i	\(0.208226\pi\)
\(7\)	−0.0961645	+	0.483452i	−0.0363468	+	0.182728i	−0.994694	−	0.102878i	\(-0.967195\pi\)
							0.958347	+	0.285606i	\(0.0921948\pi\)
\(11\)	0.665312	−	3.24921i	0.200599	−	0.979673i
							\(13\)	3.73794	+	3.73794i	1.03672	+	1.03672i	0.999300	+	0.0374183i	\(0.0119134\pi\)
0.0374183	+	0.999300i	\(0.488087\pi\)
\(17\)	1.76850	+	3.72457i	0.428925	+	0.903340i
							\(19\)	−2.61249	−	1.08213i	−0.599346	−	0.248257i	0.0623194	−	0.998056i	\(-0.480150\pi\)
−0.661666	+	0.749799i	\(0.730150\pi\)
\(23\)	1.16869	−	0.780895i	0.243689	−	0.162828i	−0.427728	−	0.903907i	\(-0.640686\pi\)
							0.671417	+	0.741080i	\(0.265686\pi\)
\(29\)	−5.15194	+	1.02478i	−0.956691	+	0.190298i	−0.648660	−	0.761079i	\(-0.724670\pi\)
							−0.308031	+	0.951376i	\(0.599670\pi\)
\(31\)	−2.24939	+	3.36645i	−0.404002	+	0.604632i	−0.976563	−	0.215230i	\(-0.930950\pi\)
							0.572561	+	0.819862i	\(0.305950\pi\)
\(37\)	1.99647	+	1.33400i	0.328218	+	0.219308i	0.708750	−	0.705459i	\(-0.249259\pi\)
							−0.380532	+	0.924768i	\(0.624259\pi\)
\(41\)	−1.70551	+	8.57417i	−0.266356	+	1.33906i	0.583529	+	0.812092i	\(0.301671\pi\)
							−0.849885	+	0.526968i	\(0.823329\pi\)
\(43\)	1.89153	−	0.783499i	0.288456	−	0.119482i	−0.233763	−	0.972293i	\(-0.575104\pi\)
							0.522220	+	0.852811i	\(0.325104\pi\)
\(47\)	−0.833247	+	0.833247i	−0.121542	+	0.121542i	−0.765261	−	0.643720i	\(-0.777390\pi\)
							0.643720	+	0.765261i	\(0.277390\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.m.a.10.11	yes	128
11.10	odd	2	inner	187.2.m.a.10.6	✓	128
17.12	odd	16	inner	187.2.m.a.131.6	yes	128
187.131	even	16	inner	187.2.m.a.131.11	yes	128

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.m.a.10.6	✓	128	11.10	odd	2	inner
187.2.m.a.10.11	yes	128	1.1	even	1	trivial
187.2.m.a.131.6	yes	128	17.12	odd	16	inner
187.2.m.a.131.11	yes	128	187.131	even	16	inner