Embedded newform 121.2.e.a.23.6

• Label: 121.2.e.a.23.6
• 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			23.6
Character	\(\chi\)	\(=\)	121.23
Dual form			121.2.e.a.100.6

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.194417 - 0.425713i) q^{2} -3.09292 q^{3} +(1.16629 + 1.34597i) q^{4} +(1.44135 + 0.423218i) q^{5} +(-0.601314 + 1.31669i) q^{6} +(0.384441 + 2.67384i) q^{7} +(1.69784 - 0.498530i) q^{8} +6.56613 q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 6 q^{2} - 18 q^{3} - 16 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} + 4 q^{8} + 70 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.194417	−	0.425713i	0.137473	−	0.301024i	−0.828357	−	0.560201i	\(-0.810724\pi\)
							0.965830	+	0.259177i	\(0.0834512\pi\)
\(3\)	−3.09292			−1.78570			−0.892848	−	0.450358i	\(-0.851296\pi\)
							−0.892848	+	0.450358i	\(0.851296\pi\)
\(5\)	1.44135	+	0.423218i	0.644590	+	0.189269i	0.587658	−	0.809109i	\(-0.300050\pi\)
							0.0569321	+	0.998378i	\(0.481868\pi\)
\(7\)	0.384441	+	2.67384i	0.145305	+	1.01062i	0.923775	+	0.382936i	\(0.125087\pi\)
							−0.778470	+	0.627682i	\(0.784004\pi\)
\(11\)	1.33791	+	3.03480i	0.403395	+	0.915026i
							\(13\)	−3.28970	−	3.79652i	−0.912400	−	1.05297i	−0.998393	−	0.0566697i	\(-0.981952\pi\)
0.0859932	−	0.996296i	\(-0.472594\pi\)
\(17\)	2.89312	+	1.85929i	0.701684	+	0.450945i	0.842222	−	0.539130i	\(-0.181247\pi\)
							−0.140538	+	0.990075i	\(0.544883\pi\)
\(19\)	−4.00764	+	2.57555i	−0.919415	+	0.590872i	−0.912488	−	0.409104i	\(-0.865841\pi\)
							−0.00692729	+	0.999976i	\(0.502205\pi\)
\(23\)	0.906958	−	6.30803i	0.189114	−	1.31532i	−0.645195	−	0.764018i	\(-0.723224\pi\)
							0.834308	−	0.551298i	\(-0.185867\pi\)
\(29\)	2.04739	−	1.31578i	0.380191	−	0.244334i	−0.336562	−	0.941661i	\(-0.609264\pi\)
							0.716753	+	0.697328i	\(0.245628\pi\)
\(31\)	4.55302	−	5.25447i	0.817747	−	0.943731i	−0.181466	−	0.983397i	\(-0.558084\pi\)
							0.999213	+	0.0396665i	\(0.0126296\pi\)
\(37\)	1.84892	−	2.13377i	0.303961	−	0.350789i	−0.583135	−	0.812375i	\(-0.698174\pi\)
							0.887095	+	0.461586i	\(0.152719\pi\)
\(41\)	−0.623819	+	1.36597i	−0.0974242	+	0.213329i	−0.952069	−	0.305885i	\(-0.901048\pi\)
							0.854644	+	0.519214i	\(0.173775\pi\)
\(43\)	−0.381636	+	0.112058i	−0.0581990	+	0.0170888i	−0.310702	−	0.950507i	\(-0.600564\pi\)
							0.252503	+	0.967596i	\(0.418746\pi\)
\(47\)	−1.38166	−	3.02540i	−0.201535	−	0.441301i	0.781697	−	0.623658i	\(-0.214354\pi\)
							−0.983232	+	0.182358i	\(0.941627\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.2.e.a.23.6	✓	100
121.100	even	11	inner	121.2.e.a.100.6	yes	100

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.2.e.a.23.6	✓	100	1.1	even	1	trivial
121.2.e.a.100.6	yes	100	121.100	even	11	inner