Embedded newform 23.11.d.a.5.18

• Label: 23.11.d.a.5.18
• 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			5.18
Character	\(\chi\)	\(=\)	23.5
Dual form			23.11.d.a.14.18

$q$-expansion

\(f(q)\)	\(=\)	\(q+(57.4680 + 16.8741i) q^{2} +(42.8012 - 49.3952i) q^{3} +(2156.39 + 1385.83i) q^{4} +(-2527.86 - 363.452i) q^{5} +(3293.20 - 2116.41i) q^{6} +(28411.7 - 12975.2i) q^{7} +(60375.3 + 69676.8i) q^{8} +(7795.60 + 54219.6i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 190 q + 13 q^{2} - 71 q^{3} - 11699 q^{4} - 11 q^{5} + 3346 q^{6} - 11 q^{7} - 50582 q^{8} - 394850 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	57.4680	+	16.8741i	1.79588	+	0.527317i	0.997223	−	0.0744754i	\(-0.0237282\pi\)
							0.798653	+	0.601792i	\(0.205546\pi\)
\(3\)	42.8012	−	49.3952i	0.176137	−	0.203273i	−0.660816	−	0.750548i	\(-0.729790\pi\)
							0.836953	+	0.547276i	\(0.184335\pi\)
\(5\)	−2527.86	−	363.452i	−0.808916	−	0.116305i	−0.274567	−	0.961568i	\(-0.588534\pi\)
							−0.534350	+	0.845264i	\(0.679443\pi\)
\(7\)	28411.7	−	12975.2i	1.69047	−	0.772010i	0.691708	−	0.722177i	\(-0.256858\pi\)
							0.998758	−	0.0498329i	\(-0.0158689\pi\)
\(11\)	25801.7	+	87872.6i	0.160208	+	0.545620i	0.999996	+	0.00270516i	\(0.000861082\pi\)
							−0.839788	+	0.542915i	\(0.817321\pi\)
\(13\)	−71595.6	+	156772.i	−0.192828	+	0.422234i	−0.981208	−	0.192955i	\(-0.938193\pi\)
							0.788380	+	0.615189i	\(0.210920\pi\)
\(17\)	−1.48984e6	−	2.31824e6i	−1.04929	−	1.63273i	−0.727760	−	0.685832i	\(-0.759439\pi\)
							−0.321532	−	0.946899i	\(-0.604198\pi\)
\(19\)	712762.	−	1.10908e6i	0.287857	−	0.447914i	−0.666967	−	0.745087i	\(-0.732408\pi\)
							0.954823	+	0.297174i	\(0.0960441\pi\)
\(23\)	−5.42172e6	+	3.46864e6i	−0.842361	+	0.538914i
							\(29\)	1.49361e7	−	9.59883e6i	0.728192	−	0.467981i	−0.123286	−	0.992371i	\(-0.539343\pi\)
0.851478	+	0.524390i	\(0.175707\pi\)
\(31\)	−1.68851e7	−	1.94864e7i	−0.589786	−	0.680649i	0.379894	−	0.925030i	\(-0.375961\pi\)
							−0.969679	+	0.244381i	\(0.921415\pi\)
\(37\)	5.89426e6	−	847467.i	0.0850004	−	0.0122212i	−0.0996834	−	0.995019i	\(-0.531783\pi\)
							0.184684	+	0.982798i	\(0.440874\pi\)
\(41\)	5.60753e6	−	3.90012e7i	0.0484008	−	0.336635i	−0.951205	−	0.308559i	\(-0.900153\pi\)
							0.999606	−	0.0280752i	\(-0.00893780\pi\)
\(43\)	−2.19165e7	−	1.89908e7i	−0.149084	−	0.129182i	0.577126	−	0.816655i	\(-0.304174\pi\)
							−0.726209	+	0.687474i	\(0.758720\pi\)
\(47\)	−1.85457e8			−0.808639			−0.404320	−	0.914618i	\(-0.632492\pi\)
							−0.404320	+	0.914618i	\(0.632492\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.11.d.a.5.18	✓	190
23.14	odd	22	inner	23.11.d.a.14.18	yes	190

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.11.d.a.5.18	✓	190	1.1	even	1	trivial
23.11.d.a.14.18	yes	190	23.14	odd	22	inner