Embedded newform 187.2.m.a.10.1

• Label: 187.2.m.a.10.1
• 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			10.1
Character	\(\chi\)	\(=\)	187.10
Dual form			187.2.m.a.131.1

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.31737 - 0.959888i) q^{2} +(0.0998402 + 0.0667111i) q^{3} +(3.03462 + 3.03462i) q^{4} +(-1.55498 + 0.309305i) q^{5} +(-0.167332 - 0.250430i) q^{6} +(-0.0889145 + 0.447003i) q^{7} +(-2.19968 - 5.31050i) q^{8} +(-1.14253 - 2.75832i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.31737	−	0.959888i	−1.63863	−	0.678743i	−0.642472	−	0.766309i	\(-0.722091\pi\)
							−0.996159	+	0.0875663i	\(0.972091\pi\)
\(3\)	0.0998402	+	0.0667111i	0.0576427	+	0.0385157i	0.584058	−	0.811712i	\(-0.301464\pi\)
							−0.526415	+	0.850228i	\(0.676464\pi\)
\(5\)	−1.55498	+	0.309305i	−0.695409	+	0.138325i	−0.530124	−	0.847920i	\(-0.677854\pi\)
							−0.165285	+	0.986246i	\(0.552854\pi\)
\(7\)	−0.0889145	+	0.447003i	−0.0336065	+	0.168951i	−0.993944	−	0.109890i	\(-0.964950\pi\)
							0.960337	+	0.278841i	\(0.0899502\pi\)
\(11\)	−0.793239	−	3.22037i	−0.239170	−	0.970978i
							\(13\)	0.499494	+	0.499494i	0.138535	+	0.138535i	0.772973	−	0.634439i	\(-0.218769\pi\)
−0.634439	+	0.772973i	\(0.718769\pi\)
\(17\)	−3.56112	−	2.07808i	−0.863699	−	0.504008i
							\(19\)	−5.37514	−	2.22646i	−1.23314	−	0.510784i	−0.331578	−	0.943428i	\(-0.607581\pi\)
−0.901565	+	0.432643i	\(0.857581\pi\)
\(23\)	−3.29905	+	2.20436i	−0.687900	+	0.459640i	−0.849757	−	0.527174i	\(-0.823252\pi\)
							0.161857	+	0.986814i	\(0.448252\pi\)
\(29\)	3.31573	−	0.659540i	0.615716	−	0.122473i	0.122627	−	0.992453i	\(-0.460868\pi\)
							0.493088	+	0.869979i	\(0.335868\pi\)
\(31\)	3.16065	−	4.73025i	0.567670	−	0.849578i	−0.430935	−	0.902383i	\(-0.641816\pi\)
							0.998605	+	0.0528053i	\(0.0168163\pi\)
\(37\)	−4.33899	−	2.89922i	−0.713325	−	0.476629i	0.145198	−	0.989403i	\(-0.453618\pi\)
							−0.858524	+	0.512774i	\(0.828618\pi\)
\(41\)	1.25379	−	6.30321i	0.195808	−	0.984396i	−0.750436	−	0.660943i	\(-0.770156\pi\)
							0.946244	−	0.323452i	\(-0.104844\pi\)
\(43\)	4.62051	−	1.91388i	0.704622	−	0.291864i	−0.00145533	−	0.999999i	\(-0.500463\pi\)
							0.706077	+	0.708135i	\(0.250463\pi\)
\(47\)	−5.30782	+	5.30782i	−0.774225	+	0.774225i	−0.978842	−	0.204617i	\(-0.934405\pi\)
							0.204617	+	0.978842i	\(0.434405\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.m.a.10.1	✓	128
11.10	odd	2	inner	187.2.m.a.10.16	yes	128
17.12	odd	16	inner	187.2.m.a.131.16	yes	128
187.131	even	16	inner	187.2.m.a.131.1	yes	128

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.m.a.10.1	✓	128	1.1	even	1	trivial
187.2.m.a.10.16	yes	128	11.10	odd	2	inner
187.2.m.a.131.1	yes	128	187.131	even	16	inner
187.2.m.a.131.16	yes	128	17.12	odd	16	inner