Embedded newform 287.3.y.a.10.19

• Label: 287.3.y.a.10.19
• 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			10.19
Character	\(\chi\)	\(=\)	287.10
Dual form			287.3.y.a.201.19

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.153412 + 1.45962i) q^{2} +(0.632396 + 0.365114i) q^{3} +(1.80565 + 0.383802i) q^{4} +(2.72179 + 2.45071i) q^{5} +(-0.629943 + 0.867043i) q^{6} +(4.21354 - 5.58982i) q^{7} +(-2.65133 + 8.15997i) q^{8} +(-4.23338 - 7.33244i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q - 3 q^{2} - 24 q^{3} + 101 q^{4} - 9 q^{5} - 6 q^{7} - 16 q^{8} + 576 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.153412	+	1.45962i	−0.0767059	+	0.729808i	0.886806	+	0.462142i	\(0.152919\pi\)
							−0.963512	+	0.267666i	\(0.913748\pi\)
\(3\)	0.632396	+	0.365114i	0.210799	+	0.121705i	0.601682	−	0.798735i	\(-0.294497\pi\)
							−0.390884	+	0.920440i	\(0.627831\pi\)
\(5\)	2.72179	+	2.45071i	0.544357	+	0.490141i	0.894815	−	0.446437i	\(-0.147307\pi\)
							−0.350458	+	0.936579i	\(0.613974\pi\)
\(7\)	4.21354	−	5.58982i	0.601934	−	0.798546i
							\(11\)	13.5398	+	15.0374i	1.23089	+	1.36704i	0.907104	+	0.420907i	\(0.138288\pi\)
0.323783	+	0.946131i	\(0.395045\pi\)
\(13\)	2.31655	−	3.18845i	0.178196	−	0.245266i	−0.710570	−	0.703626i	\(-0.751563\pi\)
							0.888766	+	0.458360i	\(0.151563\pi\)
\(17\)	−0.245688	+	0.221219i	−0.0144523	+	0.0130129i	−0.676325	−	0.736603i	\(-0.736429\pi\)
							0.661873	+	0.749616i	\(0.269762\pi\)
\(19\)	5.91942	−	13.2952i	0.311549	−	0.699750i	−0.688117	−	0.725600i	\(-0.741563\pi\)
							0.999666	+	0.0258498i	\(0.00822917\pi\)
\(23\)	−1.05825	+	10.0685i	−0.0460107	+	0.437763i	0.947131	+	0.320847i	\(0.103967\pi\)
							−0.993142	+	0.116916i	\(0.962699\pi\)
\(29\)	0.457890	+	1.40924i	0.0157893	+	0.0485945i	0.958641	−	0.284619i	\(-0.0918671\pi\)
							−0.942851	+	0.333213i	\(0.891867\pi\)
\(31\)	−41.3854	+	37.2636i	−1.33501	+	1.20205i	−0.373392	+	0.927674i	\(0.621805\pi\)
							−0.961622	+	0.274378i	\(0.911528\pi\)
\(37\)	−9.78730	+	10.8699i	−0.264522	+	0.293781i	−0.860744	−	0.509039i	\(-0.830001\pi\)
							0.596222	+	0.802819i	\(0.296668\pi\)
\(41\)	29.5090	+	28.4644i	0.719731	+	0.694253i
							\(43\)	26.8761	+	19.5266i	0.625026	+	0.454108i	0.854674	−	0.519166i	\(-0.173757\pi\)
−0.229647	+	0.973274i	\(0.573757\pi\)
\(47\)	−2.43989	−	0.256443i	−0.0519126	−	0.00545624i	0.0785365	−	0.996911i	\(-0.474975\pi\)
							−0.130449	+	0.991455i	\(0.541642\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.y.a.10.19	✓	432
7.5	odd	6	inner	287.3.y.a.215.36	yes	432
41.37	even	5	inner	287.3.y.a.283.36	yes	432
287.201	odd	30	inner	287.3.y.a.201.19	yes	432

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.y.a.10.19	✓	432	1.1	even	1	trivial
287.3.y.a.201.19	yes	432	287.201	odd	30	inner
287.3.y.a.215.36	yes	432	7.5	odd	6	inner
287.3.y.a.283.36	yes	432	41.37	even	5	inner