Embedded newform 183.2.g.c.50.9

• Label: 183.2.g.c.50.9
• 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			50.9
Character	\(\chi\)	\(=\)	183.50
Dual form			183.2.g.c.11.9

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.379018 + 0.379018i) q^{2} +(0.171716 - 1.72352i) q^{3} -1.71269i q^{4} -3.88753 q^{5} +(0.718327 - 0.588160i) q^{6} +(-0.228336 + 0.228336i) q^{7} +(1.40718 - 1.40718i) q^{8} +(-2.94103 - 0.591911i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.379018	+	0.379018i	0.268006	+	0.268006i	0.828296	−	0.560290i	\(-0.189310\pi\)
							−0.560290	+	0.828296i	\(0.689310\pi\)
\(3\)	0.171716	−	1.72352i	0.0991403	−	0.995073i
							\(5\)	−3.88753			−1.73856			−0.869278	−	0.494324i	\(-0.835416\pi\)
−0.869278	+	0.494324i	\(0.835416\pi\)
\(7\)	−0.228336	+	0.228336i	−0.0863029	+	0.0863029i	−0.748940	−	0.662637i	\(-0.769437\pi\)
							0.662637	+	0.748940i	\(0.269437\pi\)
\(11\)	0.950712	−	0.950712i	0.286650	−	0.286650i	−0.549104	−	0.835754i	\(-0.685031\pi\)
							0.835754	+	0.549104i	\(0.185031\pi\)
\(13\)	3.36668			0.933748			0.466874	−	0.884324i	\(-0.345380\pi\)
							0.466874	+	0.884324i	\(0.345380\pi\)
\(17\)	2.30066	−	2.30066i	0.557992	−	0.557992i	−0.370744	−	0.928735i	\(-0.620897\pi\)
							0.928735	+	0.370744i	\(0.120897\pi\)
\(19\)		−	2.69380i		−	0.617999i	−0.951062	−	0.309000i	\(-0.900006\pi\)
							0.951062	−	0.309000i	\(-0.0999942\pi\)
\(23\)	1.83535	+	1.83535i	0.382697	+	0.382697i	0.872073	−	0.489376i	\(-0.162775\pi\)
							−0.489376	+	0.872073i	\(0.662775\pi\)
\(29\)	6.51667	−	6.51667i	1.21012	−	1.21012i	0.239127	−	0.970988i	\(-0.423139\pi\)
							0.970988	−	0.239127i	\(-0.0768612\pi\)
\(31\)	4.27632	+	4.27632i	0.768050	+	0.768050i	0.977763	−	0.209713i	\(-0.0672530\pi\)
							−0.209713	+	0.977763i	\(0.567253\pi\)
\(37\)	−1.99865	−	1.99865i	−0.328576	−	0.328576i	0.523469	−	0.852045i	\(-0.324638\pi\)
							−0.852045	+	0.523469i	\(0.824638\pi\)
\(41\)	−10.7872			−1.68467			−0.842337	−	0.538951i	\(-0.818821\pi\)
							−0.842337	+	0.538951i	\(0.818821\pi\)
\(43\)	−1.53106	−	1.53106i	−0.233485	−	0.233485i	0.580661	−	0.814146i	\(-0.302794\pi\)
							−0.814146	+	0.580661i	\(0.802794\pi\)
\(47\)			5.44307i			0.793954i	0.917829	+	0.396977i	\(0.129941\pi\)
							−0.917829	+	0.396977i	\(0.870059\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	183.2.g.c.50.9	yes	28
3.2	odd	2	inner	183.2.g.c.50.6	yes	28
61.11	odd	4	inner	183.2.g.c.11.6	✓	28
183.11	even	4	inner	183.2.g.c.11.9	yes	28

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
183.2.g.c.11.6	✓	28	61.11	odd	4	inner
183.2.g.c.11.9	yes	28	183.11	even	4	inner
183.2.g.c.50.6	yes	28	3.2	odd	2	inner
183.2.g.c.50.9	yes	28	1.1	even	1	trivial