Embedded newform 121.2.e.a.23.5

• Label: 121.2.e.a.23.5
• Level: $121$
• Weight: $2$
• Character: 121.23
• Analytic conductor: $0.966$
• Analytic rank: $0$
• Dimension: $100$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	121.e (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.966189864457\)
Analytic rank:	\(0\)
Dimension:	\(100\)
Relative dimension:	\(10\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			23.5
Character	\(\chi\)	\(=\)	121.23
Dual form			121.2.e.a.100.5

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.389908 + 0.853778i) q^{2} +1.43258 q^{3} +(0.732812 + 0.845710i) q^{4} +(0.815711 + 0.239514i) q^{5} +(-0.558572 + 1.22310i) q^{6} +(-0.497109 - 3.45747i) q^{7} +(-2.80893 + 0.824777i) q^{8} -0.947723 q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 6 q^{2} - 18 q^{3} - 16 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} + 4 q^{8} + 70 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/121\mathbb{Z}\right)^\times\).

\(n\)	\(2\)
\(\chi(n)\)	\(e\left(\frac{7}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.389908	+	0.853778i	−0.275706	+	0.603712i	−0.995940	−	0.0900189i	\(-0.971307\pi\)
							0.720234	+	0.693731i	\(0.244035\pi\)
\(3\)	1.43258			0.827099			0.413549	−	0.910482i	\(-0.364289\pi\)
							0.413549	+	0.910482i	\(0.364289\pi\)
\(5\)	0.815711	+	0.239514i	0.364797	+	0.107114i	0.458994	−	0.888440i	\(-0.348210\pi\)
							−0.0941966	+	0.995554i	\(0.530028\pi\)
\(7\)	−0.497109	−	3.45747i	−0.187890	−	1.30680i	−0.837459	−	0.546499i	\(-0.815960\pi\)
							0.649570	−	0.760302i	\(-0.274949\pi\)
\(11\)	1.66261	+	2.86979i	0.501296	+	0.865276i
							\(13\)	−1.40374	−	1.62001i	−0.389328	−	0.449309i	0.526923	−	0.849913i	\(-0.323346\pi\)
−0.916251	+	0.400604i	\(0.868800\pi\)
\(17\)	−0.588906	−	0.378467i	−0.142831	−	0.0917917i	0.467274	−	0.884113i	\(-0.345236\pi\)
							−0.610105	+	0.792321i	\(0.708873\pi\)
\(19\)	−0.622832	+	0.400270i	−0.142887	+	0.0918282i	−0.610131	−	0.792300i	\(-0.708883\pi\)
							0.467244	+	0.884128i	\(0.345247\pi\)
\(23\)	−0.0418652	+	0.291179i	−0.00872949	+	0.0607149i	−0.993721	−	0.111890i	\(-0.964309\pi\)
							0.984991	+	0.172605i	\(0.0552185\pi\)
\(29\)	5.58409	−	3.58868i	1.03694	−	0.666400i	0.0927114	−	0.995693i	\(-0.470447\pi\)
							0.944228	+	0.329293i	\(0.106810\pi\)
\(31\)	−0.108218	+	0.124890i	−0.0194365	+	0.0224309i	−0.765385	−	0.643573i	\(-0.777451\pi\)
							0.745948	+	0.666004i	\(0.231997\pi\)
\(37\)	7.15405	−	8.25621i	1.17612	−	1.35731i	0.255519	−	0.966804i	\(-0.417754\pi\)
							0.920599	−	0.390509i	\(-0.127701\pi\)
\(41\)	−1.70125	+	3.72521i	−0.265690	+	0.581780i	−0.994711	−	0.102711i	\(-0.967248\pi\)
							0.729021	+	0.684491i	\(0.239975\pi\)
\(43\)	−4.25261	+	1.24868i	−0.648516	+	0.190422i	−0.589415	−	0.807830i	\(-0.700642\pi\)
							−0.0591013	+	0.998252i	\(0.518824\pi\)
\(47\)	3.26155	+	7.14181i	0.475747	+	1.04174i	0.983611	+	0.180303i	\(0.0577078\pi\)
							−0.507865	+	0.861437i	\(0.669565\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.2.e.a.23.5	✓	100
121.100	even	11	inner	121.2.e.a.100.5	yes	100

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.2.e.a.23.5	✓	100	1.1	even	1	trivial
121.2.e.a.100.5	yes	100	121.100	even	11	inner