Embedded newform 187.2.m.a.10.14

• Label: 187.2.m.a.10.14
• 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			10.14
Character	\(\chi\)	\(=\)	187.10
Dual form			187.2.m.a.131.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.58527 + 0.656642i) q^{2} +(2.26689 + 1.51468i) q^{3} +(0.667703 + 0.667703i) q^{4} +(-3.74296 + 0.744522i) q^{5} +(2.59903 + 3.88972i) q^{6} +(0.334093 - 1.67960i) q^{7} +(-0.693234 - 1.67362i) q^{8} +(1.69645 + 4.09559i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.58527	+	0.656642i	1.12096	+	0.464316i	0.864698	−	0.502292i	\(-0.167510\pi\)
							0.256260	+	0.966608i	\(0.417510\pi\)
\(3\)	2.26689	+	1.51468i	1.30879	+	0.874504i	0.997131	−	0.0756916i	\(-0.0241164\pi\)
							0.311656	+	0.950195i	\(0.399116\pi\)
\(5\)	−3.74296	+	0.744522i	−1.67390	+	0.332960i	−0.938660	−	0.344843i	\(-0.887932\pi\)
							−0.735243	+	0.677803i	\(0.762932\pi\)
\(7\)	0.334093	−	1.67960i	0.126275	−	0.634829i	−0.864864	−	0.502006i	\(-0.832596\pi\)
							0.991140	−	0.132823i	\(-0.0424043\pi\)
\(11\)	3.21741	−	0.805138i	0.970087	−	0.242758i
							\(13\)	2.69751	+	2.69751i	0.748155	+	0.748155i	0.974132	−	0.225978i	\(-0.0725577\pi\)
−0.225978	+	0.974132i	\(0.572558\pi\)
\(17\)	−1.14497	−	3.96094i	−0.277696	−	0.960669i
							\(19\)	−4.05978	−	1.68161i	−0.931377	−	0.385789i	−0.135176	−	0.990822i	\(-0.543160\pi\)
−0.796201	+	0.605033i	\(0.793160\pi\)
\(23\)	−3.79941	+	2.53868i	−0.792231	+	0.529352i	−0.884587	−	0.466374i	\(-0.845560\pi\)
							0.0923567	+	0.995726i	\(0.470560\pi\)
\(29\)	−6.63760	+	1.32030i	−1.23257	+	0.245174i	−0.768051	−	0.640389i	\(-0.778773\pi\)
							−0.464520	+	0.885563i	\(0.653773\pi\)
\(31\)	−2.57365	+	3.85173i	−0.462241	+	0.691792i	−0.987227	−	0.159319i	\(-0.949070\pi\)
							0.524987	+	0.851110i	\(0.324070\pi\)
\(37\)	4.11189	+	2.74748i	0.675990	+	0.451682i	0.845592	−	0.533830i	\(-0.179248\pi\)
							−0.169601	+	0.985513i	\(0.554248\pi\)
\(41\)	−1.90465	+	9.57533i	−0.297457	+	1.49542i	0.485995	+	0.873962i	\(0.338457\pi\)
							−0.783451	+	0.621453i	\(0.786543\pi\)
\(43\)	3.15691	−	1.30764i	0.481425	−	0.199413i	−0.128754	−	0.991677i	\(-0.541098\pi\)
							0.610179	+	0.792264i	\(0.291098\pi\)
\(47\)	−3.85758	+	3.85758i	−0.562685	+	0.562685i	−0.930069	−	0.367384i	\(-0.880253\pi\)
							0.367384	+	0.930069i	\(0.380253\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.m.a.10.14	yes	128
11.10	odd	2	inner	187.2.m.a.10.3	✓	128
17.12	odd	16	inner	187.2.m.a.131.3	yes	128
187.131	even	16	inner	187.2.m.a.131.14	yes	128

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.m.a.10.3	✓	128	11.10	odd	2	inner
187.2.m.a.10.14	yes	128	1.1	even	1	trivial
187.2.m.a.131.3	yes	128	17.12	odd	16	inner
187.2.m.a.131.14	yes	128	187.131	even	16	inner