Embedded newform 483.2.y.b.340.14

• Label: 483.2.y.b.340.14
• Level: $483$
• Weight: $2$
• Character: 483.340
• Analytic conductor: $3.857$
• Analytic rank: $0$
• Dimension: $320$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.y (of order \(33\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.85677441763\)
Analytic rank:	\(0\)
Dimension:	\(320\)
Relative dimension:	\(16\) over \(\Q(\zeta_{33})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			340.14
Character	\(\chi\)	\(=\)	483.340
Dual form			483.2.y.b.331.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.543075 + 2.23858i) q^{2} +(-0.327068 - 0.945001i) q^{3} +(-2.93866 + 1.51498i) q^{4} +(0.848567 - 0.339715i) q^{5} +(1.93784 - 1.24538i) q^{6} +(-1.85432 + 1.88719i) q^{7} +(-1.97036 - 2.27392i) q^{8} +(-0.786053 + 0.618159i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 2 q^{2} + 16 q^{3} + 18 q^{4} - 2 q^{5} + 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\)	\(323\)	\(346\)	\(442\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{6}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.543075	+	2.23858i	0.384012	+	1.58292i	0.755930	+	0.654653i	\(0.227185\pi\)
							−0.371918	+	0.928266i	\(0.621300\pi\)
\(3\)	−0.327068	−	0.945001i	−0.188833	−	0.545596i
							\(5\)	0.848567	−	0.339715i	0.379491	−	0.151925i	−0.174071	−	0.984733i	\(-0.555692\pi\)
0.553562	+	0.832808i	\(0.313268\pi\)
\(7\)	−1.85432	+	1.88719i	−0.700866	+	0.713293i
							\(11\)	−0.391524	+	1.61388i	−0.118049	+	0.486604i	0.881838	+	0.471553i	\(0.156306\pi\)
−0.999887	+	0.0150513i	\(0.995209\pi\)
\(13\)	−0.956434	+	2.09430i	−0.265267	+	0.580854i	−0.994656	−	0.103246i	\(-0.967077\pi\)
							0.729389	+	0.684099i	\(0.239804\pi\)
\(17\)	0.203713	+	4.27647i	0.0494077	+	1.03720i	0.878397	+	0.477931i	\(0.158613\pi\)
							−0.828990	+	0.559264i	\(0.811084\pi\)
\(19\)	−0.0510087	+	1.07080i	−0.0117022	+	0.245659i	0.985435	+	0.170050i	\(0.0543931\pi\)
							−0.997138	+	0.0756088i	\(0.975910\pi\)
\(23\)	−3.48578	−	3.29384i	−0.726835	−	0.686812i
							\(29\)	−1.08851	+	0.699545i	−0.202132	+	0.129902i	−0.637791	−	0.770209i	\(-0.720152\pi\)
0.435659	+	0.900112i	\(0.356515\pi\)
\(31\)	10.6451	−	2.05168i	1.91192	−	0.368492i	0.912721	−	0.408584i	\(-0.133977\pi\)
							0.999196	+	0.0400922i	\(0.0127652\pi\)
\(37\)	1.07090	−	0.842163i	0.176055	−	0.138451i	−0.526243	−	0.850334i	\(-0.676400\pi\)
							0.702298	+	0.711883i	\(0.252157\pi\)
\(41\)	−0.771391	+	5.36514i	−0.120471	+	0.837894i	0.836553	+	0.547886i	\(0.184567\pi\)
							−0.957024	+	0.290008i	\(0.906342\pi\)
\(43\)	5.22204	−	6.02656i	0.796354	−	0.919041i	−0.201822	−	0.979422i	\(-0.564686\pi\)
							0.998175	+	0.0603812i	\(0.0192316\pi\)
\(47\)	−1.20372	−	2.08490i	−0.175580	−	0.304114i	0.764782	−	0.644289i	\(-0.222847\pi\)
							−0.940362	+	0.340176i	\(0.889513\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.y.b.340.14	yes	320
7.2	even	3	inner	483.2.y.b.478.14	yes	320
23.9	even	11	inner	483.2.y.b.193.14	✓	320
161.9	even	33	inner	483.2.y.b.331.14	yes	320

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.y.b.193.14	✓	320	23.9	even	11	inner
483.2.y.b.331.14	yes	320	161.9	even	33	inner
483.2.y.b.340.14	yes	320	1.1	even	1	trivial
483.2.y.b.478.14	yes	320	7.2	even	3	inner