Embedded newform 190.3.o.a.29.18

• Label: 190.3.o.a.29.18
• Level: $190$
• Weight: $3$
• Character: 190.29
• Analytic conductor: $5.177$
• Analytic rank: $0$
• Dimension: $120$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	190.o (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.17712502285\)
Analytic rank:	\(0\)
Dimension:	\(120\)
Relative dimension:	\(20\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.18
Character	\(\chi\)	\(=\)	190.29
Dual form			190.3.o.a.59.18

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.245576 + 1.39273i) q^{2} +(2.27829 - 1.91171i) q^{3} +(-1.87939 + 0.684040i) q^{4} +(4.99661 + 0.184101i) q^{5} +(3.22199 + 2.70357i) q^{6} +(5.25836 + 3.03592i) q^{7} +(-1.41421 - 2.44949i) q^{8} +(-0.0268715 + 0.152396i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/190\mathbb{Z}\right)^\times\).

\(n\)	\(21\)	\(77\)
\(\chi(n)\)	\(e\left(\frac{17}{18}\right)\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.245576	+	1.39273i	0.122788	+	0.696364i
							\(3\)	2.27829	−	1.91171i	0.759430	−	0.637238i	−0.178548	−	0.983931i	\(-0.557140\pi\)
0.937978	+	0.346694i	\(0.112696\pi\)
\(5\)	4.99661	+	0.184101i	0.999322	+	0.0368203i
							\(7\)	5.25836	+	3.03592i	0.751195	+	0.433703i	0.826125	−	0.563486i	\(-0.190540\pi\)
−0.0749306	+	0.997189i	\(0.523874\pi\)
\(11\)	−9.74263	−	16.8747i	−0.885694	−	1.53407i	−0.844916	−	0.534899i	\(-0.820350\pi\)
							−0.0407779	−	0.999168i	\(-0.512984\pi\)
\(13\)	5.74434	+	4.82007i	0.441872	+	0.370775i	0.836409	−	0.548105i	\(-0.184651\pi\)
							−0.394537	+	0.918880i	\(0.629095\pi\)
\(17\)	20.1323	−	3.54987i	1.18425	−	0.208816i	0.453372	−	0.891321i	\(-0.350221\pi\)
							0.730880	+	0.682505i	\(0.239110\pi\)
\(19\)	−4.21253	+	18.5271i	−0.221712	+	0.975112i
							\(23\)	1.27413	+	3.50063i	0.0553967	+	0.152201i	0.964304	−	0.264796i	\(-0.0853046\pi\)
−0.908908	+	0.416997i	\(0.863082\pi\)
\(29\)	−24.0718	−	4.24451i	−0.830063	−	0.146363i	−0.257557	−	0.966263i	\(-0.582918\pi\)
							−0.572506	+	0.819901i	\(0.694029\pi\)
\(31\)	−41.6156	−	24.0268i	−1.34244	−	0.775057i	−0.355273	−	0.934763i	\(-0.615612\pi\)
							−0.987165	+	0.159706i	\(0.948945\pi\)
\(37\)	−27.9811			−0.756246			−0.378123	−	0.925755i	\(-0.623430\pi\)
							−0.378123	+	0.925755i	\(0.623430\pi\)
\(41\)	12.6885	+	15.1215i	0.309474	+	0.368817i	0.898254	−	0.439476i	\(-0.144836\pi\)
							−0.588780	+	0.808293i	\(0.700391\pi\)
\(43\)	3.50850	−	9.63954i	0.0815931	−	0.224175i	−0.892187	−	0.451666i	\(-0.850830\pi\)
							0.973780	+	0.227491i	\(0.0730521\pi\)
\(47\)	−65.3897	−	11.5300i	−1.39127	−	0.245319i	−0.572719	−	0.819752i	\(-0.694111\pi\)
							−0.818551	+	0.574433i	\(0.805222\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	190.3.o.a.29.18	yes	120
5.4	even	2	inner	190.3.o.a.29.3	✓	120
19.2	odd	18	inner	190.3.o.a.59.3	yes	120
95.59	odd	18	inner	190.3.o.a.59.18	yes	120

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.3.o.a.29.3	✓	120	5.4	even	2	inner
190.3.o.a.29.18	yes	120	1.1	even	1	trivial
190.3.o.a.59.3	yes	120	19.2	odd	18	inner
190.3.o.a.59.18	yes	120	95.59	odd	18	inner