Embedded newform 235.4.g.b.196.18

• Label: 235.4.g.b.196.18
• Level: $235$
• Weight: $4$
• Character: 235.196
• Analytic conductor: $13.865$
• Analytic rank: $0$
• Dimension: $550$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 235 = 5 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	235.g (of order \(23\), degree \(22\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(13.8654488513\)
Analytic rank:	\(0\)
Dimension:	\(550\)
Relative dimension:	\(25\) over \(\Q(\zeta_{23})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{23}]$

Embedding invariants

Embedding label			196.18
Character	\(\chi\)	\(=\)	235.196
Dual form			235.4.g.b.6.18

$q$-expansion

\(f(q)\)	\(=\)	\(q+(2.47081 + 1.07322i) q^{2} +(-0.351491 - 5.13861i) q^{3} +(-0.507353 - 0.543242i) q^{4} +(-4.27210 - 2.59792i) q^{5} +(4.64641 - 13.0737i) q^{6} +(-4.33565 + 20.8643i) q^{7} +(-7.88740 - 22.1930i) q^{8} +(0.466704 - 0.0641470i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 550 q + 4 q^{2} - 2 q^{3} - 102 q^{4} + 125 q^{5} + 44 q^{6} - 2 q^{7} - 6 q^{8} - 175 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/235\mathbb{Z}\right)^\times\).

\(n\)	\(142\)	\(146\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{4}{23}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	2.47081	+	1.07322i	0.873562	+	0.379441i	0.787108	−	0.616815i	\(-0.211577\pi\)
							0.0864531	+	0.996256i	\(0.472447\pi\)
\(3\)	−0.351491	−	5.13861i	−0.0676445	−	0.988927i	−0.900338	−	0.435192i	\(-0.856680\pi\)
							0.832693	−	0.553735i	\(-0.186798\pi\)
\(5\)	−4.27210	−	2.59792i	−0.382108	−	0.232365i
							\(7\)	−4.33565	+	20.8643i	−0.234103	+	1.12657i	0.683771	+	0.729696i	\(0.260339\pi\)
−0.917875	+	0.396871i	\(0.870096\pi\)
\(11\)	−23.0420	−	18.7460i	−0.631583	−	0.513831i	0.260634	−	0.965438i	\(-0.416068\pi\)
							−0.892217	+	0.451607i	\(0.850851\pi\)
\(13\)	−47.4360	+	13.2909i	−1.01203	+	0.283557i	−0.735555	−	0.677465i	\(-0.763079\pi\)
							−0.276473	+	0.961022i	\(0.589166\pi\)
\(17\)	63.2397	−	51.4493i	0.902228	−	0.734017i	−0.0622831	−	0.998059i	\(-0.519838\pi\)
							0.964511	+	0.264041i	\(0.0850556\pi\)
\(19\)	−108.389	+	65.9127i	−1.30874	+	0.795863i	−0.988463	−	0.151460i	\(-0.951603\pi\)
							−0.320278	+	0.947323i	\(0.603776\pi\)
\(23\)	−145.822	+	63.3394i	−1.32200	+	0.574225i	−0.937205	−	0.348778i	\(-0.886597\pi\)
							−0.384793	+	0.923003i	\(0.625727\pi\)
\(29\)	−135.545	−	37.9779i	−0.867934	−	0.243184i	−0.193123	−	0.981175i	\(-0.561862\pi\)
							−0.674811	+	0.737991i	\(0.735775\pi\)
\(31\)	−16.2916	+	238.174i	−0.0943888	+	1.37992i	0.673431	+	0.739250i	\(0.264820\pi\)
							−0.767820	+	0.640665i	\(0.778659\pi\)
\(37\)	−94.5373	−	133.929i	−0.420050	−	0.595075i	0.550837	−	0.834613i	\(-0.314308\pi\)
							−0.970887	+	0.239538i	\(0.923004\pi\)
\(41\)	139.294	−	391.936i	0.530587	−	1.49293i	−0.309726	−	0.950826i	\(-0.600237\pi\)
							0.840312	−	0.542102i	\(-0.182372\pi\)
\(43\)	199.460	+	213.570i	0.707381	+	0.757420i	0.978750	−	0.205055i	\(-0.0657374\pi\)
							−0.271370	+	0.962475i	\(0.587477\pi\)
\(47\)	199.917	−	252.698i	0.620444	−	0.784250i

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	235.4.g.b.196.18	yes	550
47.6	even	23	inner	235.4.g.b.6.18	✓	550

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
235.4.g.b.6.18	✓	550	47.6	even	23	inner
235.4.g.b.196.18	yes	550	1.1	even	1	trivial