Embedded newform 23.14.c.a.2.17

• Label: 23.14.c.a.2.17
• Level: $23$
• Weight: $14$
• Character: 23.2
• Analytic conductor: $24.663$
• Analytic rank: $0$
• Dimension: $250$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	23.c (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(24.6631136589\)
Analytic rank:	\(0\)
Dimension:	\(250\)
Relative dimension:	\(25\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			2.17
Character	\(\chi\)	\(=\)	23.2
Dual form			23.14.c.a.12.17

$q$-expansion

\(f(q)\)	\(=\)	\(q+(63.3663 + 40.7231i) q^{2} +(-166.481 - 1157.90i) q^{3} +(-1046.16 - 2290.76i) q^{4} +(65468.7 + 19223.3i) q^{5} +(36604.0 - 80151.5i) q^{6} +(-13228.2 + 15266.2i) q^{7} +(114811. - 798531. i) q^{8} +(216723. - 63635.6i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 250 q - 11 q^{2} - 1207 q^{3} - 114699 q^{4} - 41875 q^{5} - 125668 q^{6} + 240331 q^{7} + 562996 q^{8} - 13202058 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).

\(n\)	\(5\)
\(\chi(n)\)	\(e\left(\frac{1}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	63.3663	+	40.7231i	0.700106	+	0.449931i	0.841666	−	0.539999i	\(-0.181575\pi\)
							−0.141560	+	0.989930i	\(0.545212\pi\)
\(3\)	−166.481	−	1157.90i	−0.131849	−	0.917029i	−0.943142	−	0.332390i	\(-0.892145\pi\)
							0.811293	−	0.584640i	\(-0.198764\pi\)
\(5\)	65468.7	+	19223.3i	1.87382	+	0.550204i	0.997674	+	0.0681616i	\(0.0217134\pi\)
							0.876148	+	0.482042i	\(0.160105\pi\)
\(7\)	−13228.2	+	15266.2i	−0.0424975	+	0.0490447i	−0.776600	−	0.629994i	\(-0.783058\pi\)
							0.734103	+	0.679038i	\(0.237603\pi\)
\(11\)	−4.17575e6	+	2.68359e6i	−0.710693	+	0.456734i	−0.845388	−	0.534153i	\(-0.820631\pi\)
							0.134695	+	0.990887i	\(0.456994\pi\)
\(13\)	9.28121e6	+	1.07111e7i	0.533302	+	0.615463i	0.956911	−	0.290382i	\(-0.0937824\pi\)
							−0.423609	+	0.905845i	\(0.639237\pi\)
\(17\)	3.48681e7	−	7.63506e7i	0.350357	−	0.767175i	−0.649619	−	0.760260i	\(-0.725072\pi\)
							0.999976	−	0.00691501i	\(-0.00220113\pi\)
\(19\)	−6.72833e7	−	1.47330e8i	−0.328102	−	0.718443i	0.671646	−	0.740872i	\(-0.265587\pi\)
							−0.999748	+	0.0224285i	\(0.992860\pi\)
\(23\)	4.52277e8	−	5.47249e8i	0.637050	−	0.770823i
							\(29\)	2.17302e9	−	4.75825e9i	0.678386	−	1.48546i	−0.185958	−	0.982558i	\(-0.559539\pi\)
0.864344	−	0.502901i	\(-0.167734\pi\)
\(31\)	−8.92811e8	+	6.20963e9i	−0.180679	+	1.25665i	0.674483	+	0.738291i	\(0.264367\pi\)
							−0.855162	+	0.518361i	\(0.826542\pi\)
\(37\)	2.34718e9	−	6.89193e8i	0.150395	−	0.0441601i	−0.205668	−	0.978622i	\(-0.565937\pi\)
							0.356064	+	0.934462i	\(0.384119\pi\)
\(41\)	−2.18288e10	−	6.40952e9i	−0.717687	−	0.210732i	−0.0975561	−	0.995230i	\(-0.531103\pi\)
							−0.620131	+	0.784498i	\(0.712921\pi\)
\(43\)	−4.67879e9	−	3.25417e10i	−0.112873	−	0.785047i	−0.965101	−	0.261877i	\(-0.915659\pi\)
							0.852229	−	0.523170i	\(-0.175251\pi\)
\(47\)	−2.19614e9			−0.0297183			−0.0148592	−	0.999890i	\(-0.504730\pi\)
							−0.0148592	+	0.999890i	\(0.504730\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.14.c.a.2.17	✓	250
23.12	even	11	inner	23.14.c.a.12.17	yes	250

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.14.c.a.2.17	✓	250	1.1	even	1	trivial
23.14.c.a.12.17	yes	250	23.12	even	11	inner