Embedded newform 183.2.g.c.11.9

• Label: 183.2.g.c.11.9
• Level: $183$
• Weight: $2$
• Character: 183.11
• Analytic conductor: $1.461$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• 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			11.9
Character	\(\chi\)	\(=\)	183.11
Dual form			183.2.g.c.50.9

$q$-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 \(\left(\mathbb{Z}/183\mathbb{Z}\right)^\times\).

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

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	−0.560290	−	0.828296i	\(-0.689310\pi\)
							0.828296	+	0.560290i	\(0.189310\pi\)
\(3\)	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	0.662637	−	0.748940i	\(-0.269437\pi\)
							−0.748940	+	0.662637i	\(0.769437\pi\)
\(11\)	0.950712	+	0.950712i	0.286650	+	0.286650i	0.835754	−	0.549104i	\(-0.185031\pi\)
							−0.549104	+	0.835754i	\(0.685031\pi\)
\(13\)	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	0.928735	−	0.370744i	\(-0.120897\pi\)
							−0.370744	+	0.928735i	\(0.620897\pi\)
\(19\)			2.69380i			0.617999i	0.951062	+	0.309000i	\(0.0999942\pi\)
							−0.951062	+	0.309000i	\(0.900006\pi\)
\(23\)	1.83535	−	1.83535i	0.382697	−	0.382697i	−0.489376	−	0.872073i	\(-0.662775\pi\)
							0.872073	+	0.489376i	\(0.162775\pi\)
\(29\)	6.51667	+	6.51667i	1.21012	+	1.21012i	0.970988	+	0.239127i	\(0.0768612\pi\)
							0.239127	+	0.970988i	\(0.423139\pi\)
\(31\)	4.27632	−	4.27632i	0.768050	−	0.768050i	−0.209713	−	0.977763i	\(-0.567253\pi\)
							0.977763	+	0.209713i	\(0.0672530\pi\)
\(37\)	−1.99865	+	1.99865i	−0.328576	+	0.328576i	−0.852045	−	0.523469i	\(-0.824638\pi\)
							0.523469	+	0.852045i	\(0.324638\pi\)
\(41\)	−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	−0.814146	−	0.580661i	\(-0.802794\pi\)
							0.580661	+	0.814146i	\(0.302794\pi\)
\(47\)		−	5.44307i		−	0.793954i	−0.917829	−	0.396977i	\(-0.870059\pi\)
							0.917829	−	0.396977i	\(-0.129941\pi\)

(See \(a_n\) instead)

Twists

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

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
183.2.g.c.11.6	✓	28	3.2	odd	2	inner
183.2.g.c.11.9	yes	28	1.1	even	1	trivial
183.2.g.c.50.6	yes	28	61.50	odd	4	inner
183.2.g.c.50.9	yes	28	183.50	even	4	inner