Embedded newform 287.3.v.a.44.15

• Label: 287.3.v.a.44.15
• Level: $287$
• Weight: $3$
• Character: 287.44
• 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.v (of order \(24\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.82018358714\)
Analytic rank:	\(0\)
Dimension:	\(432\)
Relative dimension:	\(54\) over \(\Q(\zeta_{24})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			44.15
Character	\(\chi\)	\(=\)	287.44
Dual form			287.3.v.a.137.15

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.518206 - 1.93397i) q^{2} +(-0.899559 + 0.118429i) q^{3} +(-0.00760404 + 0.00439020i) q^{4} +(-3.55516 + 0.952603i) q^{5} +(0.695196 + 1.67835i) q^{6} +(5.90938 + 3.75223i) q^{7} +(-5.65063 - 5.65063i) q^{8} +(-7.89815 + 2.11630i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 48 q^{8} - 36 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(206\)	\(211\)
\(\chi(n)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{8}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.518206	−	1.93397i	−0.259103	−	0.966985i	−0.965762	−	0.259431i	\(-0.916465\pi\)
							0.706659	−	0.707555i	\(-0.250202\pi\)
\(3\)	−0.899559	+	0.118429i	−0.299853	+	0.0394764i	−0.278952	−	0.960305i	\(-0.589987\pi\)
							−0.0209014	+	0.999782i	\(0.506654\pi\)
\(5\)	−3.55516	+	0.952603i	−0.711033	+	0.190521i	−0.596167	−	0.802860i	\(-0.703310\pi\)
							−0.114866	+	0.993381i	\(0.536644\pi\)
\(7\)	5.90938	+	3.75223i	0.844197	+	0.536033i
							\(11\)	1.72342	+	13.0907i	0.156674	+	1.19006i	0.871371	+	0.490625i	\(0.163231\pi\)
−0.714697	+	0.699434i	\(0.753435\pi\)
\(13\)	1.26443	−	3.05260i	0.0972639	−	0.234816i	−0.867757	−	0.496989i	\(-0.834439\pi\)
							0.965021	+	0.262173i	\(0.0844391\pi\)
\(17\)	−13.4921	+	17.5832i	−0.793652	+	1.03431i	0.204806	+	0.978802i	\(0.434344\pi\)
							−0.998458	+	0.0555049i	\(0.982323\pi\)
\(19\)	4.59649	+	0.605140i	0.241921	+	0.0318494i	0.250511	−	0.968114i	\(-0.419401\pi\)
							−0.00859082	+	0.999963i	\(0.502735\pi\)
\(23\)	18.4288	+	10.6399i	0.801254	+	0.462604i	0.843909	−	0.536486i	\(-0.180249\pi\)
							−0.0426557	+	0.999090i	\(0.513582\pi\)
\(29\)	−14.5240	+	35.0640i	−0.500827	+	1.20910i	0.448208	+	0.893929i	\(0.352062\pi\)
							−0.949034	+	0.315173i	\(0.897938\pi\)
\(31\)	44.1382	−	25.4832i	1.42381	−	0.822039i	0.427191	−	0.904162i	\(-0.359503\pi\)
							0.996622	+	0.0821228i	\(0.0261700\pi\)
\(37\)	−18.3277	+	31.7446i	−0.495344	+	0.857961i	−0.999986	−	0.00536788i	\(-0.998291\pi\)
							0.504642	+	0.863329i	\(0.331625\pi\)
\(41\)	35.7050	+	20.1533i	0.870853	+	0.491543i
							\(43\)	26.9870	−	26.9870i	0.627604	−	0.627604i	−0.319861	−	0.947465i	\(-0.603636\pi\)
0.947465	+	0.319861i	\(0.103636\pi\)
\(47\)	−61.8210	−	8.13889i	−1.31534	−	0.173168i	−0.559996	−	0.828495i	\(-0.689197\pi\)
							−0.755345	+	0.655327i	\(0.772531\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.v.a.44.15	✓	432
7.4	even	3	inner	287.3.v.a.249.40	yes	432
41.14	odd	8	inner	287.3.v.a.219.40	yes	432
287.137	odd	24	inner	287.3.v.a.137.15	yes	432

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.v.a.44.15	✓	432	1.1	even	1	trivial
287.3.v.a.137.15	yes	432	287.137	odd	24	inner
287.3.v.a.219.40	yes	432	41.14	odd	8	inner
287.3.v.a.249.40	yes	432	7.4	even	3	inner