Embedded newform 287.3.v.a.44.17

• Label: 287.3.v.a.44.17
• 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			44.17
Character	\(\chi\)	\(=\)	287.44
Dual form			287.3.v.a.137.17

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.472042 - 1.76168i) q^{2} +(0.937698 - 0.123450i) q^{3} +(0.583396 - 0.336824i) q^{4} +(2.21585 - 0.593735i) q^{5} +(-0.660113 - 1.59365i) q^{6} +(2.05508 + 6.69153i) q^{7} +(-6.02733 - 6.02733i) q^{8} +(-7.82930 + 2.09785i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 48 q^{8} - 36 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.472042	−	1.76168i	−0.236021	−	0.880842i	−0.977686	−	0.210072i	\(-0.932630\pi\)
							0.741665	−	0.670770i	\(-0.234036\pi\)
\(3\)	0.937698	−	0.123450i	0.312566	−	0.0411501i	0.0273886	−	0.999625i	\(-0.491281\pi\)
							0.285177	+	0.958475i	\(0.407948\pi\)
\(5\)	2.21585	−	0.593735i	0.443170	−	0.118747i	−0.0303320	−	0.999540i	\(-0.509656\pi\)
							0.473502	+	0.880793i	\(0.342990\pi\)
\(7\)	2.05508	+	6.69153i	0.293583	+	0.955934i
							\(11\)	−1.60282	−	12.1746i	−0.145711	−	1.10678i	−0.895486	−	0.445090i	\(-0.853172\pi\)
0.749775	−	0.661692i	\(-0.230162\pi\)
\(13\)	7.86111	−	18.9784i	0.604701	−	1.45988i	−0.263992	−	0.964525i	\(-0.585039\pi\)
							0.868693	−	0.495351i	\(-0.164961\pi\)
\(17\)	17.6057	−	22.9442i	1.03563	−	1.34966i	0.100663	−	0.994921i	\(-0.467904\pi\)
							0.934966	−	0.354737i	\(-0.115430\pi\)
\(19\)	−5.83111	−	0.767681i	−0.306901	−	0.0404042i	−0.0244970	−	0.999700i	\(-0.507798\pi\)
							−0.282404	+	0.959296i	\(0.591132\pi\)
\(23\)	34.0029	+	19.6316i	1.47839	+	0.853548i	0.999701	−	0.0244373i	\(-0.00777940\pi\)
							0.478687	+	0.877985i	\(0.341113\pi\)
\(29\)	15.3675	−	37.1004i	0.529914	−	1.27933i	−0.401665	−	0.915787i	\(-0.631568\pi\)
							0.931579	−	0.363539i	\(-0.118432\pi\)
\(31\)	2.18725	−	1.26281i	0.0705564	−	0.0407357i	−0.464307	−	0.885674i	\(-0.653696\pi\)
							0.534863	+	0.844939i	\(0.320363\pi\)
\(37\)	22.7089	−	39.3330i	0.613755	−	1.06306i	−0.376846	−	0.926276i	\(-0.622992\pi\)
							0.990602	−	0.136779i	\(-0.0436752\pi\)
\(41\)	−36.1956	+	19.2583i	−0.882818	+	0.469714i
							\(43\)	−5.62791	+	5.62791i	−0.130882	+	0.130882i	−0.769513	−	0.638631i	\(-0.779501\pi\)
0.638631	+	0.769513i	\(0.279501\pi\)
\(47\)	7.40692	+	0.975139i	0.157594	+	0.0207476i	0.208910	−	0.977935i	\(-0.433008\pi\)
							−0.0513163	+	0.998682i	\(0.516342\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.v.a.44.17	✓	432
7.4	even	3	inner	287.3.v.a.249.38	yes	432
41.14	odd	8	inner	287.3.v.a.219.38	yes	432
287.137	odd	24	inner	287.3.v.a.137.17	yes	432

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.v.a.44.17	✓	432	1.1	even	1	trivial
287.3.v.a.137.17	yes	432	287.137	odd	24	inner
287.3.v.a.219.38	yes	432	41.14	odd	8	inner
287.3.v.a.249.38	yes	432	7.4	even	3	inner