Embedded newform 235.4.g.b.6.11

• Label: 235.4.g.b.6.11
• Level: $235$
• Weight: $4$
• Character: 235.6
• Analytic conductor: $13.865$
• Analytic rank: $0$
• Dimension: $550$
• CM: no
• 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			6.11
Character	\(\chi\)	\(=\)	235.6
Dual form			235.4.g.b.196.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.261636 + 0.113644i) q^{2} +(-0.360867 + 5.27570i) q^{3} +(-5.40489 + 5.78722i) q^{4} +(-4.27210 + 2.59792i) q^{5} +(-0.505137 - 1.42132i) q^{6} +(-7.14630 - 34.3899i) q^{7} +(1.52062 - 4.27863i) q^{8} +(-0.954221 - 0.131155i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 550 q + 4 q^{2} - 2 q^{3} - 102 q^{4} + 125 q^{5} + 44 q^{6} - 2 q^{7} - 6 q^{8} - 175 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(142\)	\(146\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{19}{23}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.261636	+	0.113644i	−0.0925021	+	0.0401793i	−0.444145	−	0.895955i	\(-0.646493\pi\)
							0.351643	+	0.936134i	\(0.385623\pi\)
\(3\)	−0.360867	+	5.27570i	−0.0694490	+	1.01531i	0.824130	+	0.566401i	\(0.191665\pi\)
							−0.893579	+	0.448907i	\(0.851814\pi\)
\(5\)	−4.27210	+	2.59792i	−0.382108	+	0.232365i
							\(7\)	−7.14630	−	34.3899i	−0.385864	−	1.85688i	−0.503746	−	0.863852i	\(-0.668045\pi\)
0.117881	−	0.993028i	\(-0.462390\pi\)
\(11\)	−13.9627	+	11.3595i	−0.382718	+	0.311365i	−0.802943	−	0.596056i	\(-0.796734\pi\)
							0.420225	+	0.907420i	\(0.361951\pi\)
\(13\)	23.9898	+	6.72164i	0.511814	+	0.143404i	0.516002	−	0.856588i	\(-0.327420\pi\)
							−0.00418739	+	0.999991i	\(0.501333\pi\)
\(17\)	−85.1093	−	69.2416i	−1.21424	−	0.987856i	−0.999939	−	0.0110879i	\(-0.996471\pi\)
							−0.214299	−	0.976768i	\(-0.568747\pi\)
\(19\)	64.5245	+	39.2382i	0.779101	+	0.473782i	0.851990	−	0.523558i	\(-0.175396\pi\)
							−0.0728886	+	0.997340i	\(0.523222\pi\)
\(23\)	14.7718	+	6.41632i	0.133919	+	0.0581693i	0.464298	−	0.885679i	\(-0.346307\pi\)
							−0.330378	+	0.943849i	\(0.607176\pi\)
\(29\)	230.708	−	64.6413i	1.47729	−	0.413917i	0.565558	−	0.824708i	\(-0.308661\pi\)
							0.911729	+	0.410792i	\(0.134748\pi\)
\(31\)	4.42886	+	64.7476i	0.0256596	+	0.375129i	0.992709	+	0.120539i	\(0.0384623\pi\)
							−0.967049	+	0.254590i	\(0.918059\pi\)
\(37\)	65.7731	−	93.1792i	0.292244	−	0.414015i	−0.644187	−	0.764868i	\(-0.722804\pi\)
							0.936431	+	0.350853i	\(0.114108\pi\)
\(41\)	−94.1231	−	264.837i	−0.358526	−	1.00880i	−0.975152	−	0.221539i	\(-0.928892\pi\)
							0.616626	−	0.787256i	\(-0.288499\pi\)
\(43\)	266.680	−	285.545i	0.945776	−	1.01268i	−0.0541244	−	0.998534i	\(-0.517237\pi\)
							0.999900	−	0.0141442i	\(-0.00450238\pi\)
\(47\)	−56.3761	−	317.246i	−0.174964	−	0.984575i

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	235.4.g.b.6.11	✓	550
47.8	even	23	inner	235.4.g.b.196.11	yes	550

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
235.4.g.b.6.11	✓	550	1.1	even	1	trivial
235.4.g.b.196.11	yes	550	47.8	even	23	inner