Embedded newform 605.2.k.b.56.19

• Label: 605.2.k.b.56.19
• Level: $605$
• Weight: $2$
• Character: 605.56
• Analytic conductor: $4.831$
• Analytic rank: $0$
• Dimension: $220$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.k (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.83094932229\)
Analytic rank:	\(0\)
Dimension:	\(220\)
Relative dimension:	\(22\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			56.19
Character	\(\chi\)	\(=\)	605.56
Dual form			605.2.k.b.551.19

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.92400 + 0.564938i) q^{2} +2.93193 q^{3} +(1.70012 + 1.09260i) q^{4} +(0.654861 - 0.755750i) q^{5} +(5.64104 + 1.65636i) q^{6} +(-0.651570 + 1.42674i) q^{7} +(0.0274874 + 0.0317221i) q^{8} +5.59624 q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q - 2 q^{2} - 24 q^{4} + 22 q^{5} + 8 q^{6} + 4 q^{7} - 6 q^{8} + 212 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\)	\(122\)	\(486\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{1}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.92400	+	0.564938i	1.36047	+	0.399471i	0.878930	−	0.476951i	\(-0.158258\pi\)
							0.481544	+	0.876422i	\(0.340076\pi\)
\(3\)	2.93193			1.69275			0.846377	−	0.532585i	\(-0.178779\pi\)
							0.846377	+	0.532585i	\(0.178779\pi\)
\(5\)	0.654861	−	0.755750i	0.292863	−	0.337981i
							\(7\)	−0.651570	+	1.42674i	−0.246270	+	0.539257i	−0.991888	−	0.127118i	\(-0.959427\pi\)
0.745617	+	0.666374i	\(0.232155\pi\)
\(11\)	−3.06154	+	1.27553i	−0.923089	+	0.384586i
							\(13\)	−4.96420	−	3.19030i	−1.37682	−	0.884829i	−0.377667	−	0.925942i	\(-0.623273\pi\)
−0.999155	+	0.0411123i	\(0.986910\pi\)
\(17\)	−0.0505884	−	0.351850i	−0.0122695	−	0.0853361i	0.982767	−	0.184851i	\(-0.0591801\pi\)
							−0.995036	+	0.0995145i	\(0.968271\pi\)
\(19\)	−0.679997	+	4.72948i	−0.156002	+	1.08502i	0.749907	+	0.661544i	\(0.230098\pi\)
							−0.905909	+	0.423473i	\(0.860811\pi\)
\(23\)	−1.14943	−	2.51689i	−0.239672	−	0.524808i	0.751126	−	0.660159i	\(-0.229511\pi\)
							−0.990798	+	0.135351i	\(0.956784\pi\)
\(29\)	−1.09373	+	7.60709i	−0.203101	+	1.41260i	0.591908	+	0.806005i	\(0.298375\pi\)
							−0.795010	+	0.606597i	\(0.792534\pi\)
\(31\)	−3.32991	+	2.14000i	−0.598069	+	0.384355i	−0.804366	−	0.594134i	\(-0.797495\pi\)
							0.206298	+	0.978489i	\(0.433859\pi\)
\(37\)	8.15207	−	5.23902i	1.34019	−	0.861289i	0.343236	−	0.939249i	\(-0.388477\pi\)
							0.996956	+	0.0779603i	\(0.0248407\pi\)
\(41\)	7.45077	+	2.18774i	1.16361	+	0.341668i	0.805836	−	0.592139i	\(-0.201716\pi\)
							0.357778	+	0.933807i	\(0.383534\pi\)
\(43\)	3.56447	+	4.11362i	0.543577	+	0.627321i	0.959374	−	0.282136i	\(-0.0910430\pi\)
							−0.415798	+	0.909457i	\(0.636498\pi\)
\(47\)	9.36944	−	2.75111i	1.36667	−	0.401291i	0.485562	−	0.874202i	\(-0.338615\pi\)
							0.881110	+	0.472911i	\(0.156797\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.k.b.56.19	✓	220
121.67	even	11	inner	605.2.k.b.551.19	yes	220

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.k.b.56.19	✓	220	1.1	even	1	trivial
605.2.k.b.551.19	yes	220	121.67	even	11	inner