Embedded newform 23.14.c.a.2.15

• Label: 23.14.c.a.2.15
• 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			2.15
Character	\(\chi\)	\(=\)	23.2
Dual form			23.14.c.a.12.15

$q$-expansion

\(f(q)\)	\(=\)	\(q+(17.0328 + 10.9463i) q^{2} +(262.763 + 1827.56i) q^{3} +(-3232.78 - 7078.81i) q^{4} +(-52729.4 - 15482.7i) q^{5} +(-15529.5 + 34004.8i) q^{6} +(-49738.1 + 57400.9i) q^{7} +(46028.4 - 320134. i) q^{8} +(-1.74119e6 + 511260. i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 250 q - 11 q^{2} - 1207 q^{3} - 114699 q^{4} - 41875 q^{5} - 125668 q^{6} + 240331 q^{7} + 562996 q^{8} - 13202058 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	17.0328	+	10.9463i	0.188188	+	0.120941i	0.631342	−	0.775504i	\(-0.282504\pi\)
							−0.443154	+	0.896445i	\(0.646141\pi\)
\(3\)	262.763	+	1827.56i	0.208102	+	1.44738i	0.779341	+	0.626600i	\(0.215554\pi\)
							−0.571239	+	0.820784i	\(0.693537\pi\)
\(5\)	−52729.4	−	15482.7i	−1.50920	−	0.443142i	−0.580591	−	0.814196i	\(-0.697178\pi\)
							−0.928611	+	0.371054i	\(0.878997\pi\)
\(7\)	−49738.1	+	57400.9i	−0.159791	+	0.184409i	−0.829999	−	0.557764i	\(-0.811659\pi\)
							0.670208	+	0.742173i	\(0.266205\pi\)
\(11\)	8.27330e6	−	5.31693e6i	1.40808	−	0.904916i	0.408109	−	0.912933i	\(-0.366188\pi\)
							0.999968	+	0.00801703i	\(0.00255193\pi\)
\(13\)	7.91660e6	+	9.13624e6i	0.454890	+	0.524972i	0.936147	−	0.351608i	\(-0.114365\pi\)
							−0.481257	+	0.876580i	\(0.659820\pi\)
\(17\)	−2.30436e7	+	5.04585e7i	−0.231544	+	0.507010i	−0.989365	−	0.145452i	\(-0.953536\pi\)
							0.757822	+	0.652462i	\(0.226264\pi\)
\(19\)	1.01379e8	+	2.21988e8i	0.494365	+	1.08251i	0.978260	+	0.207382i	\(0.0664944\pi\)
							−0.483895	+	0.875126i	\(0.660778\pi\)
\(23\)	−2.65342e8	−	6.58506e8i	−0.373744	−	0.927532i
							\(29\)	2.11544e9	−	4.63216e9i	0.660409	−	1.44609i	−0.221732	−	0.975108i	\(-0.571171\pi\)
0.882141	−	0.470986i	\(-0.156102\pi\)
\(31\)	1.96429e8	−	1.36619e9i	0.0397515	−	0.276478i	−0.960245	−	0.279159i	\(-0.909944\pi\)
							0.999996	+	0.00268113i	\(0.000853430\pi\)
\(37\)	1.21107e10	−	3.55602e9i	0.775993	−	0.227852i	0.130326	−	0.991471i	\(-0.458398\pi\)
							0.645667	+	0.763619i	\(0.276579\pi\)
\(41\)	3.49583e10	+	1.02647e10i	1.14936	+	0.337482i	0.800289	−	0.599614i	\(-0.204679\pi\)
							0.349070	+	0.937097i	\(0.386498\pi\)
\(43\)	−7.03018e9	−	4.88960e10i	−0.169598	−	1.17958i	−0.879716	−	0.475499i	\(-0.842267\pi\)
							0.710118	−	0.704083i	\(-0.248642\pi\)
\(47\)	1.18326e11			1.60119			0.800594	−	0.599207i	\(-0.204517\pi\)
							0.800594	+	0.599207i	\(0.204517\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.14.c.a.2.15	✓	250
23.12	even	11	inner	23.14.c.a.12.15	yes	250

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.14.c.a.2.15	✓	250	1.1	even	1	trivial
23.14.c.a.12.15	yes	250	23.12	even	11	inner