Embedded newform 23.11.d.a.5.15

• Label: 23.11.d.a.5.15
• 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			5.15
Character	\(\chi\)	\(=\)	23.5
Dual form			23.11.d.a.14.15

$q$-expansion

\(f(q)\)	\(=\)	\(q+(32.9159 + 9.66497i) q^{2} +(294.618 - 340.007i) q^{3} +(128.599 + 82.6457i) q^{4} +(-4739.48 - 681.434i) q^{5} +(12983.8 - 8344.16i) q^{6} +(-428.091 + 195.502i) q^{7} +(-19570.3 - 22585.3i) q^{8} +(-20401.6 - 141896. i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 190 q + 13 q^{2} - 71 q^{3} - 11699 q^{4} - 11 q^{5} + 3346 q^{6} - 11 q^{7} - 50582 q^{8} - 394850 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	32.9159	+	9.66497i	1.02862	+	0.302030i	0.752150	−	0.658992i	\(-0.229017\pi\)
							0.276471	+	0.961022i	\(0.410835\pi\)
\(3\)	294.618	−	340.007i	1.21242	−	1.39921i	0.320355	−	0.947298i	\(-0.396198\pi\)
							0.892064	−	0.451909i	\(-0.149257\pi\)
\(5\)	−4739.48	−	681.434i	−1.51663	−	0.218059i	−0.666851	−	0.745191i	\(-0.732358\pi\)
							−0.849783	+	0.527132i	\(0.823267\pi\)
\(7\)	−428.091	+	195.502i	−0.0254710	+	0.0116322i	−0.428110	−	0.903727i	\(-0.640820\pi\)
							0.402639	+	0.915359i	\(0.368093\pi\)
\(11\)	59359.4	+	202160.i	0.368575	+	1.25525i	0.910037	+	0.414527i	\(0.136053\pi\)
							−0.541462	+	0.840725i	\(0.682129\pi\)
\(13\)	51959.9	−	113776.i	0.139943	−	0.306433i	−0.826664	−	0.562696i	\(-0.809764\pi\)
							0.966607	+	0.256263i	\(0.0824914\pi\)
\(17\)	430520.	+	669902.i	0.303214	+	0.471810i	0.959107	−	0.283044i	\(-0.0913442\pi\)
							−0.655893	+	0.754854i	\(0.727708\pi\)
\(19\)	2.10932e6	−	3.28216e6i	0.851872	−	1.32554i	−0.0921806	−	0.995742i	\(-0.529384\pi\)
							0.944052	−	0.329796i	\(-0.106980\pi\)
\(23\)	4.23407e6	−	4.84759e6i	0.657839	−	0.753159i
							\(29\)	2.71507e7	−	1.74487e7i	1.32370	−	0.850692i	0.328124	−	0.944634i	\(-0.393583\pi\)
0.995578	+	0.0939428i	\(0.0299471\pi\)
\(31\)	−1.14124e7	−	1.31707e7i	−0.398630	−	0.460043i	0.520579	−	0.853813i	\(-0.325716\pi\)
							−0.919209	+	0.393770i	\(0.871171\pi\)
\(37\)	−6.16059e7	+	8.85760e6i	−0.888411	+	0.127734i	−0.571385	−	0.820682i	\(-0.693593\pi\)
							−0.317026	+	0.948417i	\(0.602684\pi\)
\(41\)	578086.	−	4.02068e6i	0.00498969	−	0.0347040i	−0.987174	−	0.159645i	\(-0.948965\pi\)
							0.992164	+	0.124941i	\(0.0398741\pi\)
\(43\)	5.22933e7	+	4.53124e7i	0.355716	+	0.308230i	0.814326	−	0.580408i	\(-0.197107\pi\)
							−0.458610	+	0.888638i	\(0.651652\pi\)
\(47\)	1.89341e8			0.825573			0.412786	−	0.910828i	\(-0.364556\pi\)
							0.412786	+	0.910828i	\(0.364556\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.11.d.a.5.15	✓	190
23.14	odd	22	inner	23.11.d.a.14.15	yes	190

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.11.d.a.5.15	✓	190	1.1	even	1	trivial
23.11.d.a.14.15	yes	190	23.14	odd	22	inner