Embedded newform 23.11.d.a.5.1

• Label: 23.11.d.a.5.1
• 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			5.1
Character	\(\chi\)	\(=\)	23.5
Dual form			23.11.d.a.14.1

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-56.2787 - 16.5249i) q^{2} +(234.062 - 270.123i) q^{3} +(2032.78 + 1306.39i) q^{4} +(-3980.54 - 572.315i) q^{5} +(-17636.5 + 11334.3i) q^{6} +(21107.4 - 9639.44i) q^{7} +(-53481.6 - 61721.0i) q^{8} +(-9777.37 - 68003.1i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 190 q + 13 q^{2} - 71 q^{3} - 11699 q^{4} - 11 q^{5} + 3346 q^{6} - 11 q^{7} - 50582 q^{8} - 394850 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−56.2787	−	16.5249i	−1.75871	−	0.516404i	−0.766638	−	0.642080i	\(-0.778072\pi\)
							−0.992071	+	0.125676i	\(0.959890\pi\)
\(3\)	234.062	−	270.123i	0.963220	−	1.11162i	−0.0304791	−	0.999535i	\(-0.509703\pi\)
							0.993699	−	0.112080i	\(-0.0357512\pi\)
\(5\)	−3980.54	−	572.315i	−1.27377	−	0.183141i	−0.527944	−	0.849279i	\(-0.677037\pi\)
							−0.745828	+	0.666139i	\(0.767946\pi\)
\(7\)	21107.4	−	9639.44i	1.25587	−	0.573537i	0.327381	−	0.944892i	\(-0.393834\pi\)
							0.928491	+	0.371355i	\(0.121107\pi\)
\(11\)	−36497.5	−	124299.i	−0.226621	−	0.771800i	−0.991780	−	0.127958i	\(-0.959158\pi\)
							0.765158	−	0.643842i	\(-0.222661\pi\)
\(13\)	221688.	−	485428.i	0.597069	−	1.30740i	−0.334006	−	0.942571i	\(-0.608401\pi\)
							0.931075	−	0.364828i	\(-0.118872\pi\)
\(17\)	−809118.	−	1.25901e6i	−0.569859	−	0.886717i	0.430012	−	0.902823i	\(-0.358509\pi\)
							−0.999870	+	0.0161061i	\(0.994873\pi\)
\(19\)	−1.65242e6	+	2.57121e6i	−0.667347	+	1.03841i	0.328243	+	0.944593i	\(0.393544\pi\)
							−0.995589	+	0.0938184i	\(0.970093\pi\)
\(23\)	5.09282e6	+	3.93569e6i	0.791260	+	0.611480i
							\(29\)	−1.28934e7	+	8.28607e6i	−0.628604	+	0.403979i	−0.815792	−	0.578345i	\(-0.803699\pi\)
0.187189	+	0.982324i	\(0.440062\pi\)
\(31\)	−1.37135e7	−	1.58263e7i	−0.479006	−	0.552802i	0.463889	−	0.885894i	\(-0.346454\pi\)
							−0.942895	+	0.333091i	\(0.891908\pi\)
\(37\)	−3.37799e7	+	4.85682e6i	−0.487136	+	0.0700396i	−0.381507	−	0.924366i	\(-0.624595\pi\)
							−0.105629	+	0.994406i	\(0.533686\pi\)
\(41\)	−1.97021e7	+	1.37031e8i	−0.170056	+	1.18277i	0.708704	+	0.705506i	\(0.249280\pi\)
							−0.878761	+	0.477263i	\(0.841629\pi\)
\(43\)	−5.16788e6	−	4.47799e6i	−0.0351536	−	0.0304608i	0.637107	−	0.770776i	\(-0.280131\pi\)
							−0.672260	+	0.740315i	\(0.734676\pi\)
\(47\)	−1.50330e8			−0.655477			−0.327738	−	0.944769i	\(-0.606286\pi\)
							−0.327738	+	0.944769i	\(0.606286\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.11.d.a.5.1	✓	190
23.14	odd	22	inner	23.11.d.a.14.1	yes	190

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.11.d.a.5.1	✓	190	1.1	even	1	trivial
23.11.d.a.14.1	yes	190	23.14	odd	22	inner