Embedded newform 23.10.c.a.2.3

• Label: 23.10.c.a.2.3
• Level: $23$
• Weight: $10$
• Character: 23.2
• Analytic conductor: $11.846$
• Analytic rank: $0$
• Dimension: $170$
• CM: no
• Inner twists: $2$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(11.8458242318\)
Analytic rank:	\(0\)
Dimension:	\(170\)
Relative dimension:	\(17\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			2.3
Character	\(\chi\)	\(=\)	23.2
Dual form			23.10.c.a.12.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-26.6551 - 17.1302i) q^{2} +(-29.0863 - 202.300i) q^{3} +(204.359 + 447.484i) q^{4} +(210.621 + 61.8440i) q^{5} +(-2690.14 + 5890.58i) q^{6} +(-3087.20 + 3562.81i) q^{7} +(-90.4594 + 629.159i) q^{8} +(-21193.5 + 6222.98i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 170 q - 43 q^{2} - 157 q^{3} - 4619 q^{4} + 2265 q^{5} + 1532 q^{6} + 8605 q^{7} - 28412 q^{8} - 84756 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−26.6551	−	17.1302i	−1.17800	−	0.757055i	−0.202983	−	0.979182i	\(-0.565064\pi\)
							−0.975018	+	0.222127i	\(0.928700\pi\)
\(3\)	−29.0863	−	202.300i	−0.207321	−	1.44195i	−0.781851	−	0.623466i	\(-0.785724\pi\)
							0.574530	−	0.818484i	\(-0.305185\pi\)
\(5\)	210.621	+	61.8440i	0.150708	+	0.0442520i	0.356217	−	0.934403i	\(-0.384067\pi\)
							−0.205508	+	0.978655i	\(0.565885\pi\)
\(7\)	−3087.20	+	3562.81i	−0.485985	+	0.560857i	−0.944788	−	0.327681i	\(-0.893733\pi\)
							0.458803	+	0.888538i	\(0.348278\pi\)
\(11\)	−18225.4	+	11712.8i	−0.375327	+	0.241208i	−0.714681	−	0.699451i	\(-0.753428\pi\)
							0.339354	+	0.940659i	\(0.389792\pi\)
\(13\)	35840.8	+	41362.4i	0.348042	+	0.401662i	0.902598	−	0.430484i	\(-0.141657\pi\)
							−0.554556	+	0.832147i	\(0.687112\pi\)
\(17\)	−15804.9	+	34607.9i	−0.0458956	+	0.100497i	−0.931191	−	0.364532i	\(-0.881229\pi\)
							0.885295	+	0.465029i	\(0.153956\pi\)
\(19\)	217968.	+	477284.i	0.383709	+	0.840206i	0.998666	+	0.0516449i	\(0.0164464\pi\)
							−0.614956	+	0.788561i	\(0.710826\pi\)
\(23\)	−209752.	−	1.32558e6i	−0.156290	−	0.987711i
							\(29\)	−492000.	+	1.07733e6i	−0.129174	+	0.282851i	−0.963157	−	0.268938i	\(-0.913327\pi\)
0.833984	+	0.551789i	\(0.186055\pi\)
\(31\)	−1.12336e6	+	7.81312e6i	−0.218469	+	1.51949i	0.525223	+	0.850965i	\(0.323982\pi\)
							−0.743692	+	0.668523i	\(0.766927\pi\)
\(37\)	−2.30001e6	+	675343.i	−0.201754	+	0.0592402i	−0.381048	−	0.924555i	\(-0.624437\pi\)
							0.179294	+	0.983795i	\(0.442619\pi\)
\(41\)	2.19181e7	+	6.43573e6i	1.21136	+	0.355689i	0.824188	−	0.566317i	\(-0.191632\pi\)
							0.387177	+	0.922005i	\(0.373450\pi\)
\(43\)	2.13073e6	+	1.48195e7i	0.0950430	+	0.661038i	0.980529	+	0.196373i	\(0.0629163\pi\)
							−0.885486	+	0.464665i	\(0.846175\pi\)
\(47\)	3.65935e7			1.09386			0.546932	−	0.837177i	\(-0.315796\pi\)
							0.546932	+	0.837177i	\(0.315796\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.10.c.a.2.3	✓	170
23.12	even	11	inner	23.10.c.a.12.3	yes	170

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.10.c.a.2.3	✓	170	1.1	even	1	trivial
23.10.c.a.12.3	yes	170	23.12	even	11	inner