Embedded newform 23.11.d.a.5.7

• Label: 23.11.d.a.5.7
• 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			5.7
Character	\(\chi\)	\(=\)	23.5
Dual form			23.11.d.a.14.7

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-24.8561 - 7.29842i) q^{2} +(190.277 - 219.591i) q^{3} +(-296.883 - 190.795i) q^{4} +(3173.14 + 456.228i) q^{5} +(-6332.21 + 4069.47i) q^{6} +(23554.6 - 10757.0i) q^{7} +(23358.5 + 26957.1i) q^{8} +(-3611.46 - 25118.2i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 190 q + 13 q^{2} - 71 q^{3} - 11699 q^{4} - 11 q^{5} + 3346 q^{6} - 11 q^{7} - 50582 q^{8} - 394850 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−24.8561	−	7.29842i	−0.776754	−	0.228076i	−0.130756	−	0.991415i	\(-0.541740\pi\)
							−0.645998	+	0.763339i	\(0.723559\pi\)
\(3\)	190.277	−	219.591i	0.783032	−	0.903667i	−0.214292	−	0.976770i	\(-0.568745\pi\)
							0.997324	+	0.0731024i	\(0.0232900\pi\)
\(5\)	3173.14	+	456.228i	1.01540	+	0.145993i	0.629870	−	0.776701i	\(-0.283108\pi\)
							0.385534	+	0.922694i	\(0.374017\pi\)
\(7\)	23554.6	−	10757.0i	1.40147	−	0.640032i	0.435860	−	0.900014i	\(-0.356444\pi\)
							0.965613	+	0.259983i	\(0.0837169\pi\)
\(11\)	70344.7	+	239572.i	0.436785	+	1.48755i	0.824546	+	0.565794i	\(0.191430\pi\)
							−0.387761	+	0.921760i	\(0.626751\pi\)
\(13\)	115597.	−	253121.i	0.311336	−	0.681730i	−0.687684	−	0.726011i	\(-0.741372\pi\)
							0.999019	+	0.0442808i	\(0.0140996\pi\)
\(17\)	482169.	+	750270.i	0.339590	+	0.528412i	0.968483	−	0.249080i	\(-0.0801281\pi\)
							−0.628893	+	0.777492i	\(0.716492\pi\)
\(19\)	1.87443e6	−	2.91668e6i	0.757011	−	1.17793i	−0.222183	−	0.975005i	\(-0.571318\pi\)
							0.979194	−	0.202927i	\(-0.0650455\pi\)
\(23\)	−965446.	−	6.36352e6i	−0.149999	−	0.988686i
							\(29\)	−2.69919e7	+	1.73467e7i	−1.31596	+	0.845718i	−0.994854	−	0.101323i	\(-0.967692\pi\)
−0.321110	+	0.947042i	\(0.604056\pi\)
\(31\)	1.06002e6	+	1.22332e6i	0.0370258	+	0.0427300i	0.773960	−	0.633234i	\(-0.218273\pi\)
							−0.736935	+	0.675964i	\(0.763727\pi\)
\(37\)	−4.62127e7	+	6.64439e6i	−0.666428	+	0.0958178i	−0.467222	−	0.884140i	\(-0.654745\pi\)
							−0.199205	+	0.979958i	\(0.563836\pi\)
\(41\)	−7.10431e6	+	4.94116e7i	−0.0613201	+	0.426491i	0.935918	+	0.352218i	\(0.114573\pi\)
							−0.997238	+	0.0742724i	\(0.976337\pi\)
\(43\)	815671.	+	706783.i	0.00554846	+	0.00480777i	0.657631	−	0.753341i	\(-0.271559\pi\)
							−0.652082	+	0.758148i	\(0.726104\pi\)
\(47\)	−8.04393e7			−0.350735			−0.175367	−	0.984503i	\(-0.556111\pi\)
							−0.175367	+	0.984503i	\(0.556111\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.11.d.a.5.7	✓	190
23.14	odd	22	inner	23.11.d.a.14.7	yes	190

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.11.d.a.5.7	✓	190	1.1	even	1	trivial
23.11.d.a.14.7	yes	190	23.14	odd	22	inner