Embedded newform 187.2.m.a.54.2

• Label: 187.2.m.a.54.2
• Level: $187$
• Weight: $2$
• Character: 187.54
• 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			54.2
Character	\(\chi\)	\(=\)	187.54
Dual form			187.2.m.a.142.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.926579 - 2.23696i) q^{2} +(-1.59986 - 0.318232i) q^{3} +(-2.73122 + 2.73122i) q^{4} +(1.86996 + 2.79859i) q^{5} +(0.770525 + 3.87369i) q^{6} +(2.28141 + 1.52439i) q^{7} +(4.16641 + 1.72579i) q^{8} +(-0.313354 - 0.129795i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{9}+O(q^{10}) \)

Character values

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

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.926579	−	2.23696i	−0.655190	−	1.58177i	−0.805146	−	0.593076i	\(-0.797913\pi\)
							0.149956	−	0.988693i	\(-0.452087\pi\)
\(3\)	−1.59986	−	0.318232i	−0.923680	−	0.183731i	−0.289733	−	0.957108i	\(-0.593566\pi\)
							−0.633947	+	0.773376i	\(0.718566\pi\)
\(5\)	1.86996	+	2.79859i	0.836272	+	1.25157i	0.965617	+	0.259969i	\(0.0837125\pi\)
							−0.129345	+	0.991600i	\(0.541288\pi\)
\(7\)	2.28141	+	1.52439i	0.862293	+	0.576166i	0.906190	−	0.422870i	\(-0.138977\pi\)
							−0.0438970	+	0.999036i	\(0.513977\pi\)
\(11\)	0.278856	+	3.30488i	0.0840784	+	0.996459i
							\(13\)	−1.29221	+	1.29221i	−0.358394	+	0.358394i	−0.863221	−	0.504827i	\(-0.831556\pi\)
0.504827	+	0.863221i	\(0.331556\pi\)
\(17\)	−2.13859	−	3.52512i	−0.518683	−	0.854966i
							\(19\)	2.18731	+	5.28063i	0.501803	+	1.21146i	0.948501	+	0.316775i	\(0.102600\pi\)
−0.446697	+	0.894685i	\(0.647400\pi\)
\(23\)	6.30621	−	1.25438i	1.31493	−	0.261557i	0.512701	−	0.858567i	\(-0.328645\pi\)
							0.802234	+	0.597010i	\(0.203645\pi\)
\(29\)	−3.85019	−	5.76221i	−0.714962	−	1.07002i	−0.993962	−	0.109725i	\(-0.965003\pi\)
							0.279000	−	0.960291i	\(-0.409997\pi\)
\(31\)	−0.584450	+	2.93823i	−0.104970	+	0.527721i	0.892140	+	0.451758i	\(0.149203\pi\)
							−0.997111	+	0.0759629i	\(0.975797\pi\)
\(37\)	3.27986	+	0.652405i	0.539206	+	0.107255i	0.457178	−	0.889375i	\(-0.348860\pi\)
							0.0820281	+	0.996630i	\(0.473860\pi\)
\(41\)	1.57537	+	1.05263i	0.246031	+	0.164392i	0.672472	−	0.740123i	\(-0.265233\pi\)
							−0.426441	+	0.904515i	\(0.640233\pi\)
\(43\)	−2.32497	+	5.61297i	−0.354555	+	0.855970i	0.641491	+	0.767130i	\(0.278316\pi\)
							−0.996046	+	0.0888401i	\(0.971684\pi\)
\(47\)	0.752065	+	0.752065i	0.109700	+	0.109700i	0.759826	−	0.650126i	\(-0.225284\pi\)
							−0.650126	+	0.759826i	\(0.725284\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.m.a.54.2	✓	128
11.10	odd	2	inner	187.2.m.a.54.15	yes	128
17.6	odd	16	inner	187.2.m.a.142.15	yes	128
187.142	even	16	inner	187.2.m.a.142.2	yes	128

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.m.a.54.2	✓	128	1.1	even	1	trivial
187.2.m.a.54.15	yes	128	11.10	odd	2	inner
187.2.m.a.142.2	yes	128	187.142	even	16	inner
187.2.m.a.142.15	yes	128	17.6	odd	16	inner