Embedded newform 23.4.c.a.18.2

• Label: 23.4.c.a.18.2
• Level: $23$
• Weight: $4$
• Character: 23.18
• 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			18.2
Character	\(\chi\)	\(=\)	23.18
Dual form			23.4.c.a.9.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.49786 - 0.733439i) q^{2} +(2.24538 - 2.59131i) q^{3} +(-1.02864 - 0.661064i) q^{4} +(2.23195 - 15.5235i) q^{5} +(-7.50923 + 4.82589i) q^{6} +(-2.46994 - 5.40842i) q^{7} +(15.7230 + 18.1453i) q^{8} +(2.16936 + 15.0882i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 11 q^{2} - 13 q^{3} - 27 q^{4} - 19 q^{5} - 4 q^{6} - 19 q^{7} + 28 q^{8} + 24 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(5\)
\(\chi(n)\)	\(e\left(\frac{6}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.49786	−	0.733439i	−0.883128	−	0.259310i	−0.191439	−	0.981505i	\(-0.561315\pi\)
							−0.691690	+	0.722195i	\(0.743133\pi\)
\(3\)	2.24538	−	2.59131i	0.432124	−	0.498698i	−0.497368	−	0.867540i	\(-0.665700\pi\)
							0.929492	+	0.368842i	\(0.120246\pi\)
\(5\)	2.23195	−	15.5235i	0.199631	−	1.38847i	−0.605725	−	0.795674i	\(-0.707117\pi\)
							0.805356	−	0.592792i	\(-0.201974\pi\)
\(7\)	−2.46994	−	5.40842i	−0.133364	−	0.292027i	0.831154	−	0.556042i	\(-0.187681\pi\)
							−0.964519	+	0.264014i	\(0.914953\pi\)
\(11\)	20.9837	−	6.16138i	0.575167	−	0.168884i	0.0188033	−	0.999823i	\(-0.494014\pi\)
							0.556364	+	0.830939i	\(0.312196\pi\)
\(13\)	−14.2612	+	31.2277i	−0.304258	+	0.666232i	−0.998571	−	0.0534411i	\(-0.982981\pi\)
							0.694313	+	0.719673i	\(0.255708\pi\)
\(17\)	108.865	−	69.9635i	1.55316	−	0.998155i	0.568700	−	0.822545i	\(-0.307447\pi\)
							0.984460	−	0.175610i	\(-0.0561898\pi\)
\(19\)	−23.4761	−	15.0872i	−0.283462	−	0.182170i	0.391182	−	0.920313i	\(-0.372066\pi\)
							−0.674644	+	0.738143i	\(0.735703\pi\)
\(23\)	−18.9488	+	108.664i	−0.171787	+	0.985134i
							\(29\)	10.5650	−	6.78974i	0.0676510	−	0.0434767i	−0.506378	−	0.862312i	\(-0.669016\pi\)
0.574029	+	0.818835i	\(0.305380\pi\)
\(31\)	−10.3460	−	11.9399i	−0.0599418	−	0.0691765i	0.724987	−	0.688763i	\(-0.241846\pi\)
							−0.784929	+	0.619586i	\(0.787300\pi\)
\(37\)	33.6066	+	233.739i	0.149321	+	1.03855i	0.917334	+	0.398118i	\(0.130337\pi\)
							−0.768013	+	0.640434i	\(0.778754\pi\)
\(41\)	53.6680	−	373.269i	0.204428	−	1.42183i	−0.586516	−	0.809938i	\(-0.699501\pi\)
							0.790944	−	0.611889i	\(-0.209590\pi\)
\(43\)	−310.499	+	358.335i	−1.10118	+	1.27083i	−0.141435	+	0.989948i	\(0.545172\pi\)
							−0.959743	+	0.280880i	\(0.909374\pi\)
\(47\)	−547.089			−1.69790			−0.848948	−	0.528476i	\(-0.822764\pi\)
							−0.848948	+	0.528476i	\(0.822764\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.4.c.a.18.2	yes	50
3.2	odd	2		207.4.i.a.64.4		50
23.3	even	11		529.4.a.n.1.19		25
23.9	even	11	inner	23.4.c.a.9.2	✓	50
23.20	odd	22		529.4.a.m.1.19		25
69.32	odd	22		207.4.i.a.55.4		50

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.9.2	✓	50	23.9	even	11	inner
23.4.c.a.18.2	yes	50	1.1	even	1	trivial
207.4.i.a.55.4		50	69.32	odd	22
207.4.i.a.64.4		50	3.2	odd	2
529.4.a.m.1.19		25	23.20	odd	22
529.4.a.n.1.19		25	23.3	even	11