Embedded newform 182.4.m.b.43.2

• Label: 182.4.m.b.43.2
• Level: $182$
• Weight: $4$
• Character: 182.43
• Analytic conductor: $10.738$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	182.m (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(10.7383476210\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.2
Character	\(\chi\)	\(=\)	182.43
Dual form			182.4.m.b.127.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.73205 - 1.00000i) q^{2} +(-2.42922 + 4.20754i) q^{3} +(2.00000 + 3.46410i) q^{4} +13.8421i q^{5} +(8.41508 - 4.85845i) q^{6} +(6.06218 - 3.50000i) q^{7} -8.00000i q^{8} +(1.69773 + 2.94056i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} + 48 q^{4} - 48 q^{6} - 162 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/182\mathbb{Z}\right)^\times\).

\(n\)	\(15\)	\(157\)
\(\chi(n)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.73205	−	1.00000i	−0.612372	−	0.353553i
							\(3\)	−2.42922	+	4.20754i	−0.467505	+	0.809742i	−0.999311	−	0.0371245i	\(-0.988180\pi\)
0.531806	+	0.846866i	\(0.321514\pi\)
\(5\)			13.8421i			1.23808i	0.785360	+	0.619039i	\(0.212478\pi\)
							−0.785360	+	0.619039i	\(0.787522\pi\)
\(7\)	6.06218	−	3.50000i	0.327327	−	0.188982i
							\(11\)	44.8972	+	25.9214i	1.23064	+	0.710510i	0.967163	−	0.254156i	\(-0.0817977\pi\)
0.263476	+	0.964666i	\(0.415131\pi\)
\(13\)	16.3073	+	43.9440i	0.347910	+	0.937528i
							\(17\)	−52.8935	−	91.6142i	−0.754621	−	1.30704i	−0.945563	−	0.325440i	\(-0.894487\pi\)
0.190942	−	0.981601i	\(-0.438846\pi\)
\(19\)	−41.5743	+	24.0029i	−0.501989	+	0.289824i	−0.729535	−	0.683944i	\(-0.760263\pi\)
							0.227546	+	0.973767i	\(0.426930\pi\)
\(23\)	11.4244	−	19.7876i	0.103571	−	0.179391i	−0.809582	−	0.587006i	\(-0.800306\pi\)
							0.913154	+	0.407616i	\(0.133640\pi\)
\(29\)	−116.590	+	201.940i	−0.746561	+	1.29308i	0.202900	+	0.979199i	\(0.434963\pi\)
							−0.949462	+	0.313883i	\(0.898370\pi\)
\(31\)			123.298i			0.714354i	0.934037	+	0.357177i	\(0.116261\pi\)
							−0.934037	+	0.357177i	\(0.883739\pi\)
\(37\)	162.011	+	93.5372i	0.719850	+	0.415606i	0.814698	−	0.579886i	\(-0.196903\pi\)
							−0.0948472	+	0.995492i	\(0.530236\pi\)
\(41\)	−307.359	−	177.454i	−1.17077	−	0.675942i	−0.216905	−	0.976193i	\(-0.569596\pi\)
							−0.953860	+	0.300251i	\(0.902930\pi\)
\(43\)	36.4014	+	63.0490i	0.129097	+	0.223602i	0.923327	−	0.384015i	\(-0.125459\pi\)
							−0.794230	+	0.607617i	\(0.792126\pi\)
\(47\)		−	470.316i		−	1.45963i	−0.683645	−	0.729815i	\(-0.739606\pi\)
							0.683645	−	0.729815i	\(-0.260394\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	182.4.m.b.43.2	✓	24
13.6	odd	12		2366.4.a.bg.1.9		12
13.7	odd	12		2366.4.a.bd.1.9		12
13.10	even	6	inner	182.4.m.b.127.2	yes	24

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.4.m.b.43.2	✓	24	1.1	even	1	trivial
182.4.m.b.127.2	yes	24	13.10	even	6	inner
2366.4.a.bd.1.9		12	13.7	odd	12
2366.4.a.bg.1.9		12	13.6	odd	12