Embedded newform 23.14.c.a.2.4

• Label: 23.14.c.a.2.4
• 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			2.4
Character	\(\chi\)	\(=\)	23.2
Dual form			23.14.c.a.12.4

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-117.776 - 75.6898i) q^{2} +(-286.016 - 1989.28i) q^{3} +(4739.08 + 10377.1i) q^{4} +(-53672.4 - 15759.6i) q^{5} +(-116883. + 255938. i) q^{6} +(219501. - 253317. i) q^{7} +(64077.1 - 445666. i) q^{8} +(-2.34571e6 + 688762. i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 250 q - 11 q^{2} - 1207 q^{3} - 114699 q^{4} - 41875 q^{5} - 125668 q^{6} + 240331 q^{7} + 562996 q^{8} - 13202058 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−117.776	−	75.6898i	−1.30125	−	0.836262i	−0.307902	−	0.951418i	\(-0.599627\pi\)
							−0.993347	+	0.115156i	\(0.963263\pi\)
\(3\)	−286.016	−	1989.28i	−0.226518	−	1.57547i	−0.712612	−	0.701559i	\(-0.752488\pi\)
							0.486094	−	0.873907i	\(-0.338421\pi\)
\(5\)	−53672.4	−	15759.6i	−1.53619	−	0.451067i	−0.599255	−	0.800559i	\(-0.704536\pi\)
							−0.936940	+	0.349491i	\(0.886354\pi\)
\(7\)	219501.	−	253317.i	0.705177	−	0.813818i	−0.284265	−	0.958746i	\(-0.591749\pi\)
							0.989442	+	0.144928i	\(0.0462949\pi\)
\(11\)	5.62070e6	−	3.61221e6i	0.956617	−	0.614781i	0.0335574	−	0.999437i	\(-0.489316\pi\)
							0.923060	+	0.384656i	\(0.125680\pi\)
\(13\)	1.57864e7	+	1.82185e7i	0.907092	+	1.04684i	0.998696	+	0.0510447i	\(0.0162551\pi\)
							−0.0916042	+	0.995795i	\(0.529199\pi\)
\(17\)	−5.75633e7	+	1.26046e8i	−0.578399	+	1.26652i	0.363804	+	0.931475i	\(0.381478\pi\)
							−0.942203	+	0.335042i	\(0.891250\pi\)
\(19\)	8.81117e7	+	1.92938e8i	0.429670	+	0.940847i	0.993380	+	0.114874i	\(0.0366464\pi\)
							−0.563710	+	0.825973i	\(0.690626\pi\)
\(23\)	6.45149e8	−	2.96342e8i	0.908718	−	0.417410i
							\(29\)	−4.24025e8	+	9.28485e8i	−0.132374	+	0.289860i	−0.964199	−	0.265179i	\(-0.914569\pi\)
0.831825	+	0.555038i	\(0.187296\pi\)
\(31\)	−3.67270e7	+	2.55442e8i	−0.00743249	+	0.0516941i	−0.993200	−	0.116419i	\(-0.962858\pi\)
							0.985768	+	0.168113i	\(0.0537675\pi\)
\(37\)	−1.58797e10	+	4.66269e9i	−1.01749	+	0.298762i	−0.747614	−	0.664133i	\(-0.768801\pi\)
							−0.269875	+	0.962895i	\(0.586983\pi\)
\(41\)	−1.20813e9	−	3.54738e8i	−0.0397208	−	0.0116631i	0.261812	−	0.965119i	\(-0.415680\pi\)
							−0.301533	+	0.953456i	\(0.597498\pi\)
\(43\)	8.56774e9	+	5.95900e10i	0.206691	+	1.43757i	0.783857	+	0.620941i	\(0.213249\pi\)
							−0.577166	+	0.816627i	\(0.695842\pi\)
\(47\)	−7.71412e10			−1.04388			−0.521940	−	0.852982i	\(-0.674791\pi\)
							−0.521940	+	0.852982i	\(0.674791\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.14.c.a.2.4	✓	250
23.12	even	11	inner	23.14.c.a.12.4	yes	250

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.14.c.a.2.4	✓	250	1.1	even	1	trivial
23.14.c.a.12.4	yes	250	23.12	even	11	inner