Embedded newform 183.2.g.c.50.8

• Label: 183.2.g.c.50.8
• Level: $183$
• Weight: $2$
• Character: 183.50
• Analytic conductor: $1.461$
• Analytic rank: $0$
• Dimension: $28$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 183 = 3 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	183.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.46126235699\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			50.8
Character	\(\chi\)	\(=\)	183.50
Dual form			183.2.g.c.11.8

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.324526 + 0.324526i) q^{2} +(1.06918 + 1.36267i) q^{3} -1.78937i q^{4} +0.328679 q^{5} +(-0.0952453 + 0.789197i) q^{6} +(2.07564 - 2.07564i) q^{7} +(1.22975 - 1.22975i) q^{8} +(-0.713723 + 2.91386i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/183\mathbb{Z}\right)^\times\).

\(n\)	\(62\)	\(124\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{3}{4}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.324526	+	0.324526i	0.229475	+	0.229475i	0.812473	−	0.582999i	\(-0.198121\pi\)
							−0.582999	+	0.812473i	\(0.698121\pi\)
\(3\)	1.06918	+	1.36267i	0.617289	+	0.786736i
							\(5\)	0.328679			0.146990			0.0734949	−	0.997296i	\(-0.476585\pi\)
0.0734949	+	0.997296i	\(0.476585\pi\)
\(7\)	2.07564	−	2.07564i	0.784519	−	0.784519i	−0.196071	−	0.980590i	\(-0.562818\pi\)
							0.980590	+	0.196071i	\(0.0628182\pi\)
\(11\)	−2.26587	+	2.26587i	−0.683186	+	0.683186i	−0.960717	−	0.277530i	\(-0.910484\pi\)
							0.277530	+	0.960717i	\(0.410484\pi\)
\(13\)	1.52052			0.421718			0.210859	−	0.977517i	\(-0.432374\pi\)
							0.210859	+	0.977517i	\(0.432374\pi\)
\(17\)	−4.53068	+	4.53068i	−1.09885	+	1.09885i	−0.104307	+	0.994545i	\(0.533263\pi\)
							−0.994545	+	0.104307i	\(0.966737\pi\)
\(19\)		−	1.07773i		−	0.247248i	−0.992329	−	0.123624i	\(-0.960548\pi\)
							0.992329	−	0.123624i	\(-0.0394516\pi\)
\(23\)	−0.850212	−	0.850212i	−0.177281	−	0.177281i	0.612888	−	0.790170i	\(-0.290008\pi\)
							−0.790170	+	0.612888i	\(0.790008\pi\)
\(29\)	6.79842	−	6.79842i	1.26244	−	1.26244i	0.312526	−	0.949909i	\(-0.398825\pi\)
							0.949909	−	0.312526i	\(-0.101175\pi\)
\(31\)	2.17314	+	2.17314i	0.390308	+	0.390308i	0.874797	−	0.484489i	\(-0.160995\pi\)
							−0.484489	+	0.874797i	\(0.660995\pi\)
\(37\)	−1.53656	−	1.53656i	−0.252608	−	0.252608i	0.569431	−	0.822039i	\(-0.307164\pi\)
							−0.822039	+	0.569431i	\(0.807164\pi\)
\(41\)	1.05891			0.165374			0.0826868	−	0.996576i	\(-0.473650\pi\)
							0.0826868	+	0.996576i	\(0.473650\pi\)
\(43\)	−1.71617	−	1.71617i	−0.261713	−	0.261713i	0.564037	−	0.825750i	\(-0.309248\pi\)
							−0.825750	+	0.564037i	\(0.809248\pi\)
\(47\)			1.55753i			0.227189i	0.993527	+	0.113594i	\(0.0362364\pi\)
							−0.993527	+	0.113594i	\(0.963764\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	183.2.g.c.50.8	yes	28
3.2	odd	2	inner	183.2.g.c.50.7	yes	28
61.11	odd	4	inner	183.2.g.c.11.7	✓	28
183.11	even	4	inner	183.2.g.c.11.8	yes	28

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
183.2.g.c.11.7	✓	28	61.11	odd	4	inner
183.2.g.c.11.8	yes	28	183.11	even	4	inner
183.2.g.c.50.7	yes	28	3.2	odd	2	inner
183.2.g.c.50.8	yes	28	1.1	even	1	trivial