Embedded newform 460.2.q.a.11.18

• Label: 460.2.q.a.11.18
• Level: $460$
• Weight: $2$
• Character: 460.11
• Analytic conductor: $3.673$
• Analytic rank: $0$
• Dimension: $480$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.q (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.67311849298\)
Analytic rank:	\(0\)
Dimension:	\(480\)
Relative dimension:	\(48\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.18
Character	\(\chi\)	\(=\)	460.11
Dual form			460.2.q.a.251.18

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.520455 - 1.31496i) q^{2} +(-1.91127 - 0.274799i) q^{3} +(-1.45825 + 1.36876i) q^{4} +(0.281733 + 0.959493i) q^{5} +(0.633379 + 2.65627i) q^{6} +(1.03497 + 1.19442i) q^{7} +(2.55882 + 1.20517i) q^{8} +(0.698960 + 0.205233i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 4 q^{2} + 2 q^{6} + 2 q^{8} + 48 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\)	\(231\)	\(277\)	\(281\)
\(\chi(n)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.520455	−	1.31496i	−0.368017	−	0.929819i
							\(3\)	−1.91127	−	0.274799i	−1.10347	−	0.158655i	−0.433581	−	0.901115i	\(-0.642750\pi\)
−0.669891	+	0.742459i	\(0.733659\pi\)
\(5\)	0.281733	+	0.959493i	0.125995	+	0.429098i
							\(7\)	1.03497	+	1.19442i	0.391182	+	0.451448i	0.916844	−	0.399246i	\(-0.130728\pi\)
−0.525662	+	0.850693i	\(0.676182\pi\)
\(11\)	−2.60371	−	1.67330i	−0.785048	−	0.504520i	0.0856574	−	0.996325i	\(-0.472701\pi\)
							−0.870705	+	0.491805i	\(0.836337\pi\)
\(13\)	0.749855	−	0.865379i	0.207972	−	0.240013i	−0.642175	−	0.766558i	\(-0.721968\pi\)
							0.850147	+	0.526545i	\(0.176513\pi\)
\(17\)	3.41851	−	1.56118i	0.829111	−	0.378642i	0.0447894	−	0.998996i	\(-0.485738\pi\)
							0.784322	+	0.620354i	\(0.213011\pi\)
\(19\)	3.11916	−	6.83001i	0.715585	−	1.56691i	−0.104406	−	0.994535i	\(-0.533294\pi\)
							0.819990	−	0.572377i	\(-0.193979\pi\)
\(23\)	−2.65291	+	3.99526i	−0.553170	+	0.833069i
							\(29\)	−3.94218	−	8.63216i	−0.732044	−	1.60295i	−0.796215	−	0.605014i	\(-0.793168\pi\)
0.0641710	−	0.997939i	\(-0.479560\pi\)
\(31\)	−6.22495	+	0.895012i	−1.11803	+	0.160749i	−0.676462	−	0.736477i	\(-0.736488\pi\)
							−0.441571	+	0.897226i	\(0.645579\pi\)
\(37\)	2.28521	−	7.78270i	0.375686	−	1.27947i	−0.527256	−	0.849706i	\(-0.676779\pi\)
							0.902942	−	0.429762i	\(-0.141403\pi\)
\(41\)	−4.11652	+	1.20872i	−0.642892	+	0.188770i	−0.586898	−	0.809661i	\(-0.699651\pi\)
							−0.0559940	+	0.998431i	\(0.517833\pi\)
\(43\)	−0.0478060	+	0.332498i	−0.00729035	+	0.0507055i	−0.993142	−	0.116915i	\(-0.962699\pi\)
							0.985852	+	0.167621i	\(0.0536085\pi\)
\(47\)		−	7.29370i		−	1.06389i	−0.846777	−	0.531947i	\(-0.821460\pi\)
							0.846777	−	0.531947i	\(-0.178540\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.q.a.11.18	✓	480
4.3	odd	2	inner	460.2.q.a.11.35	yes	480
23.21	odd	22	inner	460.2.q.a.251.35	yes	480
92.67	even	22	inner	460.2.q.a.251.18	yes	480

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.q.a.11.18	✓	480	1.1	even	1	trivial
460.2.q.a.11.35	yes	480	4.3	odd	2	inner
460.2.q.a.251.18	yes	480	92.67	even	22	inner
460.2.q.a.251.35	yes	480	23.21	odd	22	inner