Embedded newform 23.11.d.a.5.4

• Label: 23.11.d.a.5.4
• Level: $23$
• Weight: $11$
• Character: 23.5
• Analytic conductor: $14.613$
• Analytic rank: $0$
• Dimension: $190$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.6132168115\)
Analytic rank:	\(0\)
Dimension:	\(190\)
Relative dimension:	\(19\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.4
Character	\(\chi\)	\(=\)	23.5
Dual form			23.11.d.a.14.4

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-41.5173 - 12.1906i) q^{2} +(-25.3274 + 29.2294i) q^{3} +(713.629 + 458.622i) q^{4} +(-2142.16 - 307.996i) q^{5} +(1407.85 - 904.770i) q^{6} +(-6037.55 + 2757.26i) q^{7} +(4978.81 + 5745.85i) q^{8} +(8190.67 + 56967.4i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 190 q + 13 q^{2} - 71 q^{3} - 11699 q^{4} - 11 q^{5} + 3346 q^{6} - 11 q^{7} - 50582 q^{8} - 394850 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(5\)
\(\chi(n)\)	\(e\left(\frac{1}{22}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−41.5173	−	12.1906i	−1.29741	−	0.380955i	−0.441122	−	0.897447i	\(-0.645419\pi\)
							−0.856292	+	0.516492i	\(0.827238\pi\)
\(3\)	−25.3274	+	29.2294i	−0.104228	+	0.120286i	−0.805467	−	0.592641i	\(-0.798085\pi\)
							0.701239	+	0.712927i	\(0.252631\pi\)
\(5\)	−2142.16	−	307.996i	−0.685492	−	0.0985589i	−0.209236	−	0.977865i	\(-0.567098\pi\)
							−0.476256	+	0.879306i	\(0.658007\pi\)
\(7\)	−6037.55	+	2757.26i	−0.359228	+	0.164054i	−0.586850	−	0.809696i	\(-0.699632\pi\)
							0.227622	+	0.973750i	\(0.426905\pi\)
\(11\)	24338.5	+	82889.2i	0.151123	+	0.514677i	0.999901	−	0.0140722i	\(-0.00447947\pi\)
							−0.848778	+	0.528749i	\(0.822661\pi\)
\(13\)	−58896.0	+	128964.i	−0.158624	+	0.347338i	−0.972211	−	0.234104i	\(-0.924784\pi\)
							0.813587	+	0.581443i	\(0.197512\pi\)
\(17\)	−716194.	−	1.11442e6i	−0.504412	−	0.784881i	0.491903	−	0.870650i	\(-0.336302\pi\)
							−0.996315	+	0.0857691i	\(0.972665\pi\)
\(19\)	356668.	−	554987.i	0.144044	−	0.224137i	−0.761733	−	0.647891i	\(-0.775651\pi\)
							0.905778	+	0.423753i	\(0.139288\pi\)
\(23\)	1.31917e6	−	6.29971e6i	0.204956	−	0.978771i
							\(29\)	1.45292e7	−	9.33737e6i	0.708358	−	0.455234i	−0.136212	−	0.990680i	\(-0.543493\pi\)
0.844570	+	0.535446i	\(0.179856\pi\)
\(31\)	6.98101e6	+	8.05652e6i	0.243843	+	0.281410i	0.864457	−	0.502706i	\(-0.167662\pi\)
							−0.620615	+	0.784116i	\(0.713117\pi\)
\(37\)	−3.02992e6	+	435637.i	−0.0436941	+	0.00628226i	−0.164127	−	0.986439i	\(-0.552481\pi\)
							0.120433	+	0.992721i	\(0.461572\pi\)
\(41\)	1.94599e7	−	1.35347e8i	0.167966	−	1.16823i	−0.715114	−	0.699007i	\(-0.753625\pi\)
							0.883080	−	0.469222i	\(-0.155466\pi\)
\(43\)	−5.42064e7	−	4.69701e7i	−0.368730	−	0.319506i	0.450711	−	0.892670i	\(-0.351170\pi\)
							−0.819441	+	0.573164i	\(0.805716\pi\)
\(47\)	1.54019e8			0.671559			0.335780	−	0.941941i	\(-0.391000\pi\)
							0.335780	+	0.941941i	\(0.391000\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.11.d.a.5.4	✓	190
23.14	odd	22	inner	23.11.d.a.14.4	yes	190

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.11.d.a.5.4	✓	190	1.1	even	1	trivial
23.11.d.a.14.4	yes	190	23.14	odd	22	inner