Embedded newform 23.4.c.a.6.3

• Label: 23.4.c.a.6.3
• Level: $23$
• Weight: $4$
• Character: 23.6
• Analytic conductor: $1.357$
• Analytic rank: $0$
• Dimension: $50$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	23.c (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.35704393013\)
Analytic rank:	\(0\)
Dimension:	\(50\)
Relative dimension:	\(5\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			6.3
Character	\(\chi\)	\(=\)	23.6
Dual form			23.4.c.a.4.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.308069 + 0.674576i) q^{2} +(1.68484 + 0.494713i) q^{3} +(4.87874 + 5.63037i) q^{4} +(3.36936 - 2.16536i) q^{5} +(-0.852766 + 0.984145i) q^{6} +(0.387311 - 2.69380i) q^{7} +(-10.9935 + 3.22799i) q^{8} +(-20.1199 - 12.9303i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 11 q^{2} - 13 q^{3} - 27 q^{4} - 19 q^{5} - 4 q^{6} - 19 q^{7} + 28 q^{8} + 24 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).

\(n\)	\(5\)
\(\chi(n)\)	\(e\left(\frac{9}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.308069	+	0.674576i	−0.108919	+	0.238499i	−0.956241	−	0.292581i	\(-0.905486\pi\)
							0.847322	+	0.531079i	\(0.178213\pi\)
\(3\)	1.68484	+	0.494713i	0.324247	+	0.0952075i	0.439805	−	0.898093i	\(-0.355047\pi\)
							−0.115558	+	0.993301i	\(0.536866\pi\)
\(5\)	3.36936	−	2.16536i	0.301365	−	0.193676i	−0.381215	−	0.924486i	\(-0.624494\pi\)
							0.682580	+	0.730811i	\(0.260858\pi\)
\(7\)	0.387311	−	2.69380i	0.0209128	−	0.145452i	−0.976690	−	0.214656i	\(-0.931137\pi\)
							0.997603	+	0.0692043i	\(0.0220460\pi\)
\(11\)	−15.2112	−	33.3080i	−0.416942	−	0.912975i	−0.995268	−	0.0971695i	\(-0.969021\pi\)
							0.578326	−	0.815806i	\(-0.303706\pi\)
\(13\)	−1.29233	−	8.98835i	−0.0275714	−	0.191763i	0.971381	−	0.237527i	\(-0.0763368\pi\)
							−0.998952	+	0.0457641i	\(0.985428\pi\)
\(17\)	3.08029	−	3.55485i	0.0439459	−	0.0507163i	−0.733351	−	0.679850i	\(-0.762045\pi\)
							0.777297	+	0.629134i	\(0.216590\pi\)
\(19\)	55.6414	+	64.2136i	0.671842	+	0.775348i	0.984663	−	0.174465i	\(-0.0558194\pi\)
							−0.312821	+	0.949812i	\(0.601274\pi\)
\(23\)	51.5471	−	97.5187i	0.467318	−	0.884089i
							\(29\)	−25.6557	+	29.6083i	−0.164281	+	0.189590i	−0.831921	−	0.554894i	\(-0.812759\pi\)
0.667640	+	0.744484i	\(0.267304\pi\)
\(31\)	−83.4835	+	24.5130i	−0.483680	+	0.142021i	−0.514477	−	0.857504i	\(-0.672014\pi\)
							0.0307965	+	0.999526i	\(0.490196\pi\)
\(37\)	123.946	+	79.6551i	0.550718	+	0.353925i	0.786218	−	0.617949i	\(-0.212036\pi\)
							−0.235500	+	0.971874i	\(0.575673\pi\)
\(41\)	−297.430	+	191.146i	−1.13294	+	0.728099i	−0.966173	−	0.257897i	\(-0.916971\pi\)
							−0.166772	+	0.985996i	\(0.553334\pi\)
\(43\)	335.657	+	98.5578i	1.19040	+	0.349533i	0.816175	−	0.577805i	\(-0.196090\pi\)
							0.374225	+	0.927338i	\(0.377909\pi\)
\(47\)	321.926			0.999100			0.499550	−	0.866285i	\(-0.333499\pi\)
							0.499550	+	0.866285i	\(0.333499\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.4.c.a.6.3	yes	50
3.2	odd	2		207.4.i.a.190.3		50
23.2	even	11		529.4.a.n.1.11		25
23.4	even	11	inner	23.4.c.a.4.3	✓	50
23.21	odd	22		529.4.a.m.1.11		25
69.50	odd	22		207.4.i.a.73.3		50

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.4.3	✓	50	23.4	even	11	inner
23.4.c.a.6.3	yes	50	1.1	even	1	trivial
207.4.i.a.73.3		50	69.50	odd	22
207.4.i.a.190.3		50	3.2	odd	2
529.4.a.m.1.11		25	23.21	odd	22
529.4.a.n.1.11		25	23.2	even	11