Embedded newform 287.3.y.a.10.20

• Label: 287.3.y.a.10.20
• 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			10.20
Character	\(\chi\)	\(=\)	287.10
Dual form			287.3.y.a.201.20

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.130578 + 1.24237i) q^{2} +(4.05852 + 2.34319i) q^{3} +(2.38617 + 0.507196i) q^{4} +(3.04278 + 2.73974i) q^{5} +(-3.44105 + 4.73619i) q^{6} +(-2.06147 - 6.68957i) q^{7} +(-2.48581 + 7.65054i) q^{8} +(6.48104 + 11.2255i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q - 3 q^{2} - 24 q^{3} + 101 q^{4} - 9 q^{5} - 6 q^{7} - 16 q^{8} + 576 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.130578	+	1.24237i	−0.0652889	+	0.621183i	0.912134	+	0.409892i	\(0.134433\pi\)
							−0.977423	+	0.211291i	\(0.932233\pi\)
\(3\)	4.05852	+	2.34319i	1.35284	+	0.781062i	0.988646	−	0.150262i	\(-0.0480116\pi\)
							0.364193	+	0.931324i	\(0.381345\pi\)
\(5\)	3.04278	+	2.73974i	0.608557	+	0.547947i	0.914749	−	0.404023i	\(-0.132388\pi\)
							−0.306192	+	0.951970i	\(0.599055\pi\)
\(7\)	−2.06147	−	6.68957i	−0.294495	−	0.955653i
							\(11\)	−4.48637	−	4.98262i	−0.407852	−	0.452966i	0.503866	−	0.863782i	\(-0.331911\pi\)
−0.911718	+	0.410816i	\(0.865244\pi\)
\(13\)	−4.67151	+	6.42978i	−0.359347	+	0.494598i	−0.949967	−	0.312352i	\(-0.898883\pi\)
							0.590620	+	0.806950i	\(0.298883\pi\)
\(17\)	−0.0503656	+	0.0453494i	−0.00296268	+	0.00266761i	−0.670611	−	0.741810i	\(-0.733968\pi\)
							0.667648	+	0.744477i	\(0.267301\pi\)
\(19\)	2.01944	−	4.53573i	0.106286	−	0.238723i	−0.852571	−	0.522611i	\(-0.824958\pi\)
							0.958857	+	0.283889i	\(0.0916246\pi\)
\(23\)	1.62253	−	15.4373i	0.0705447	−	0.671188i	−0.900917	−	0.433991i	\(-0.857105\pi\)
							0.971462	−	0.237196i	\(-0.0762285\pi\)
\(29\)	2.35352	+	7.24338i	0.0811558	+	0.249772i	0.983399	−	0.181455i	\(-0.0580808\pi\)
							−0.902243	+	0.431227i	\(0.858081\pi\)
\(31\)	25.3344	−	22.8112i	0.817238	−	0.735844i	−0.150281	−	0.988643i	\(-0.548018\pi\)
							0.967519	+	0.252799i	\(0.0813512\pi\)
\(37\)	13.1991	−	14.6591i	0.356733	−	0.396192i	−0.537889	−	0.843016i	\(-0.680778\pi\)
							0.894622	+	0.446823i	\(0.147445\pi\)
\(41\)	8.70095	+	40.0661i	0.212218	+	0.977222i
							\(43\)	−48.4864	−	35.2274i	−1.12759	−	0.819242i	−0.142248	−	0.989831i	\(-0.545433\pi\)
−0.985342	+	0.170589i	\(0.945433\pi\)
\(47\)	−44.6730	−	4.69532i	−0.950489	−	0.0999005i	−0.383423	−	0.923573i	\(-0.625255\pi\)
							−0.567066	+	0.823672i	\(0.691922\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.y.a.10.20	✓	432
7.5	odd	6	inner	287.3.y.a.215.35	yes	432
41.37	even	5	inner	287.3.y.a.283.35	yes	432
287.201	odd	30	inner	287.3.y.a.201.20	yes	432

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.y.a.10.20	✓	432	1.1	even	1	trivial
287.3.y.a.201.20	yes	432	287.201	odd	30	inner
287.3.y.a.215.35	yes	432	7.5	odd	6	inner
287.3.y.a.283.35	yes	432	41.37	even	5	inner