Embedded newform 287.3.y.a.10.18

• Label: 287.3.y.a.10.18
• Level: $287$
• Weight: $3$
• Character: 287.10
• Analytic conductor: $7.820$
• Analytic rank: $0$
• Dimension: $432$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.y (of order \(30\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.82018358714\)
Analytic rank:	\(0\)
Dimension:	\(432\)
Relative dimension:	\(54\) over \(\Q(\zeta_{30})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			10.18
Character	\(\chi\)	\(=\)	287.10
Dual form			287.3.y.a.201.18

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.181634 + 1.72813i) q^{2} +(-0.294892 - 0.170256i) q^{3} +(0.959146 + 0.203873i) q^{4} +(-1.02853 - 0.926089i) q^{5} +(0.347787 - 0.478687i) q^{6} +(-1.59260 + 6.81642i) q^{7} +(-2.67439 + 8.23091i) q^{8} +(-4.44203 - 7.69381i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q - 3 q^{2} - 24 q^{3} + 101 q^{4} - 9 q^{5} - 6 q^{7} - 16 q^{8} + 576 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\)	\(206\)	\(211\)
\(\chi(n)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{5}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.181634	+	1.72813i	−0.0908169	+	0.864065i	0.850371	+	0.526183i	\(0.176377\pi\)
							−0.941188	+	0.337882i	\(0.890289\pi\)
\(3\)	−0.294892	−	0.170256i	−0.0982973	−	0.0567520i	0.450046	−	0.893006i	\(-0.351408\pi\)
							−0.548343	+	0.836254i	\(0.684741\pi\)
\(5\)	−1.02853	−	0.926089i	−0.205705	−	0.185218i	0.559838	−	0.828602i	\(-0.310863\pi\)
							−0.765544	+	0.643384i	\(0.777530\pi\)
\(7\)	−1.59260	+	6.81642i	−0.227515	+	0.973775i
							\(11\)	4.65694	+	5.17206i	0.423359	+	0.470187i	0.916658	−	0.399672i	\(-0.130876\pi\)
−0.493300	+	0.869860i	\(0.664209\pi\)
\(13\)	−2.25656	+	3.10589i	−0.173582	+	0.238915i	−0.886940	−	0.461885i	\(-0.847173\pi\)
							0.713358	+	0.700800i	\(0.247173\pi\)
\(17\)	−3.11394	+	2.80380i	−0.183173	+	0.164930i	−0.755616	−	0.655015i	\(-0.772662\pi\)
							0.572443	+	0.819944i	\(0.305996\pi\)
\(19\)	−13.5260	+	30.3800i	−0.711896	+	1.59895i	0.0861022	+	0.996286i	\(0.472559\pi\)
							−0.797999	+	0.602659i	\(0.794108\pi\)
\(23\)	−1.61519	+	15.3676i	−0.0702259	+	0.668154i	0.901619	+	0.432532i	\(0.142380\pi\)
							−0.971845	+	0.235623i	\(0.924287\pi\)
\(29\)	7.17408	+	22.0796i	0.247382	+	0.761364i	0.995236	+	0.0975000i	\(0.0310846\pi\)
							−0.747853	+	0.663864i	\(0.768915\pi\)
\(31\)	−16.8298	+	15.1536i	−0.542897	+	0.488827i	−0.894343	−	0.447381i	\(-0.852357\pi\)
							0.351446	+	0.936208i	\(0.385690\pi\)
\(37\)	38.7329	−	43.0173i	1.04684	−	1.16263i	0.0604523	−	0.998171i	\(-0.480746\pi\)
							0.986384	−	0.164458i	\(-0.0525876\pi\)
\(41\)	−39.1033	+	12.3262i	−0.953738	+	0.300638i
							\(43\)	−41.3032	−	30.0085i	−0.960539	−	0.697872i	−0.00726295	−	0.999974i	\(-0.502312\pi\)
−0.953276	+	0.302101i	\(0.902312\pi\)
\(47\)	−15.1697	−	1.59440i	−0.322761	−	0.0339235i	−0.0582372	−	0.998303i	\(-0.518548\pi\)
							−0.264523	+	0.964379i	\(0.585215\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.y.a.10.18	✓	432
7.5	odd	6	inner	287.3.y.a.215.37	yes	432
41.37	even	5	inner	287.3.y.a.283.37	yes	432
287.201	odd	30	inner	287.3.y.a.201.18	yes	432

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.y.a.10.18	✓	432	1.1	even	1	trivial
287.3.y.a.201.18	yes	432	287.201	odd	30	inner
287.3.y.a.215.37	yes	432	7.5	odd	6	inner
287.3.y.a.283.37	yes	432	41.37	even	5	inner