Embedded newform 23.5.d.a.10.6

• Label: 23.5.d.a.10.6
• Level: $23$
• Weight: $5$
• Character: 23.10
• Analytic conductor: $2.378$
• Analytic rank: $0$
• Dimension: $70$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.37750915093\)
Analytic rank:	\(0\)
Dimension:	\(70\)
Relative dimension:	\(7\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			10.6
Character	\(\chi\)	\(=\)	23.10
Dual form			23.5.d.a.7.6

$q$-expansion

\(f(q)\)	\(=\)	\(q+(2.42804 + 2.80211i) q^{2} +(10.9682 + 7.04881i) q^{3} +(0.320606 - 2.22986i) q^{4} +(-27.0695 - 12.3622i) q^{5} +(6.87962 + 47.8488i) q^{6} +(-5.49864 + 18.7267i) q^{7} +(56.9329 - 36.5886i) q^{8} +(36.9662 + 80.9446i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 3 q^{2} + q^{3} - 35 q^{4} - 11 q^{5} - 110 q^{6} - 11 q^{7} + 146 q^{8} - 182 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(5\)
\(\chi(n)\)	\(e\left(\frac{3}{22}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	2.42804	+	2.80211i	0.607011	+	0.700528i	0.973186	−	0.230018i	\(-0.0738786\pi\)
							−0.366176	+	0.930546i	\(0.619333\pi\)
\(3\)	10.9682	+	7.04881i	1.21868	+	0.783201i	0.982091	−	0.188408i	\(-0.0603328\pi\)
							0.236593	+	0.971609i	\(0.423969\pi\)
\(5\)	−27.0695	−	12.3622i	−1.08278	−	0.494489i	−0.207564	−	0.978221i	\(-0.566554\pi\)
							−0.875216	+	0.483732i	\(0.839281\pi\)
\(7\)	−5.49864	+	18.7267i	−0.112217	+	0.382177i	−0.996381	−	0.0850005i	\(-0.972911\pi\)
							0.884164	+	0.467177i	\(0.154729\pi\)
\(11\)	−70.4928	−	61.0824i	−0.582585	−	0.504813i	0.312970	−	0.949763i	\(-0.398676\pi\)
							−0.895555	+	0.444950i	\(0.853222\pi\)
\(13\)	−82.0099	+	24.0803i	−0.485266	+	0.142487i	−0.515209	−	0.857065i	\(-0.672286\pi\)
							0.0299430	+	0.999552i	\(0.490467\pi\)
\(17\)	504.375	−	72.5182i	1.74524	−	0.250928i	0.805448	−	0.592667i	\(-0.201925\pi\)
							0.939795	+	0.341739i	\(0.111016\pi\)
\(19\)	−465.541	−	66.9347i	−1.28959	−	0.185415i	−0.536818	−	0.843698i	\(-0.680374\pi\)
							−0.752770	+	0.658283i	\(0.771283\pi\)
\(23\)	48.2638	+	526.794i	0.0912360	+	0.995829i
							\(29\)	227.988	+	1585.69i	0.271092	+	1.88549i	0.437177	+	0.899376i	\(0.355978\pi\)
−0.166084	+	0.986112i	\(0.553112\pi\)
\(31\)	−434.429	+	279.191i	−0.452060	+	0.290521i	−0.746791	−	0.665059i	\(-0.768406\pi\)
							0.294731	+	0.955580i	\(0.404770\pi\)
\(37\)	−1552.49	+	708.999i	−1.13403	+	0.517895i	−0.891848	−	0.452335i	\(-0.850591\pi\)
							−0.242184	+	0.970230i	\(0.577864\pi\)
\(41\)	846.757	−	1854.14i	0.503722	−	1.10300i	−0.471520	−	0.881856i	\(-0.656294\pi\)
							0.975242	−	0.221142i	\(-0.0709783\pi\)
\(43\)	−10.3747	+	16.1433i	−0.00561096	+	0.00873083i	−0.844048	−	0.536268i	\(-0.819834\pi\)
							0.838437	+	0.544999i	\(0.183470\pi\)
\(47\)	1577.94			0.714323			0.357161	−	0.934043i	\(-0.383745\pi\)
							0.357161	+	0.934043i	\(0.383745\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.5.d.a.10.6	yes	70
23.7	odd	22	inner	23.5.d.a.7.6	✓	70

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.5.d.a.7.6	✓	70	23.7	odd	22	inner
23.5.d.a.10.6	yes	70	1.1	even	1	trivial