Embedded newform 23.11.d.a.5.10

• Label: 23.11.d.a.5.10
• 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			5.10
Character	\(\chi\)	\(=\)	23.5
Dual form			23.11.d.a.14.10

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.740659 - 0.217477i) q^{2} +(-295.459 + 340.978i) q^{3} +(-860.942 - 553.294i) q^{4} +(-3454.08 - 496.622i) q^{5} +(292.990 - 188.293i) q^{6} +(-17524.4 + 8003.14i) q^{7} +(1034.97 + 1194.42i) q^{8} +(-20566.4 - 143043. i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 190 q + 13 q^{2} - 71 q^{3} - 11699 q^{4} - 11 q^{5} + 3346 q^{6} - 11 q^{7} - 50582 q^{8} - 394850 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.740659	−	0.217477i	−0.0231456	−	0.00679616i	0.270139	−	0.962821i	\(-0.412930\pi\)
							−0.293285	+	0.956025i	\(0.594748\pi\)
\(3\)	−295.459	+	340.978i	−1.21588	+	1.40320i	−0.327028	+	0.945015i	\(0.606047\pi\)
							−0.888855	+	0.458189i	\(0.848498\pi\)
\(5\)	−3454.08	−	496.622i	−1.10531	−	0.158919i	−0.434587	−	0.900630i	\(-0.643106\pi\)
							−0.670720	+	0.741711i	\(0.734015\pi\)
\(7\)	−17524.4	+	8003.14i	−1.04269	+	0.476179i	−0.861759	−	0.507317i	\(-0.830637\pi\)
							−0.180928	+	0.983496i	\(0.557910\pi\)
\(11\)	49695.1	+	169246.i	0.308567	+	1.05088i	0.957115	+	0.289710i	\(0.0935588\pi\)
							−0.648547	+	0.761175i	\(0.724623\pi\)
\(13\)	−281507.	+	616414.i	−0.758180	+	1.66018i	−0.00709611	+	0.999975i	\(0.502259\pi\)
							−0.751084	+	0.660207i	\(0.770468\pi\)
\(17\)	−557878.	−	868075.i	−0.392911	−	0.611382i	0.587292	−	0.809375i	\(-0.300194\pi\)
							−0.980203	+	0.197993i	\(0.936558\pi\)
\(19\)	479459.	−	746053.i	0.193635	−	0.301302i	−0.730837	−	0.682552i	\(-0.760870\pi\)
							0.924472	+	0.381250i	\(0.124506\pi\)
\(23\)	−5.66234e6	−	3.06013e6i	−0.879746	−	0.475445i
							\(29\)	2.42141e6	−	1.55615e6i	0.118054	−	0.0758684i	−0.480282	−	0.877114i	\(-0.659466\pi\)
0.598335	+	0.801246i	\(0.295829\pi\)
\(31\)	−1.11417e7	−	1.28582e7i	−0.389172	−	0.449129i	0.527029	−	0.849847i	\(-0.323306\pi\)
							−0.916201	+	0.400719i	\(0.868760\pi\)
\(37\)	−6.21325e7	+	8.93331e6i	−0.896005	+	0.128826i	−0.574906	−	0.818220i	\(-0.694961\pi\)
							−0.321099	+	0.947046i	\(0.604052\pi\)
\(41\)	−2.42416e7	+	1.68604e8i	−0.209239	+	1.45529i	0.566410	+	0.824124i	\(0.308332\pi\)
							−0.775649	+	0.631165i	\(0.782577\pi\)
\(43\)	1.23865e8	+	1.07330e8i	0.842571	+	0.730092i	0.964962	−	0.262390i	\(-0.0845107\pi\)
							−0.122391	+	0.992482i	\(0.539056\pi\)
\(47\)	−6.73035e7			−0.293459			−0.146730	−	0.989177i	\(-0.546875\pi\)
							−0.146730	+	0.989177i	\(0.546875\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.11.d.a.5.10	✓	190
23.14	odd	22	inner	23.11.d.a.14.10	yes	190

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.11.d.a.5.10	✓	190	1.1	even	1	trivial
23.11.d.a.14.10	yes	190	23.14	odd	22	inner