Embedded newform 95.3.n.a.41.2

• Label: 95.3.n.a.41.2
• Level: $95$
• Weight: $3$
• Character: 95.41
• Analytic conductor: $2.589$
• Analytic rank: $0$
• Dimension: $84$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	95.n (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.58856251142\)
Analytic rank:	\(0\)
Dimension:	\(84\)
Relative dimension:	\(14\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.2
Character	\(\chi\)	\(=\)	95.41
Dual form			95.3.n.a.51.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.24133 + 2.67111i) q^{2} +(-0.196899 - 0.540977i) q^{3} +(-1.41669 - 8.03443i) q^{4} +(-0.388289 + 2.20210i) q^{5} +(1.88632 + 0.686566i) q^{6} +(-6.30582 - 10.9220i) q^{7} +(12.5572 + 7.24989i) q^{8} +(6.64051 - 5.57205i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 12 q^{3} - 6 q^{4} + 42 q^{6} + 36 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

\(n\)	\(21\)	\(77\)
\(\chi(n)\)	\(e\left(\frac{13}{18}\right)\)	\(1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.24133	+	2.67111i	−1.12066	+	1.33555i	−0.184969	+	0.982744i	\(0.559218\pi\)
							−0.935695	+	0.352810i	\(0.885226\pi\)
\(3\)	−0.196899	−	0.540977i	−0.0656331	−	0.180326i	0.902541	−	0.430605i	\(-0.141700\pi\)
							−0.968174	+	0.250279i	\(0.919478\pi\)
\(5\)	−0.388289	+	2.20210i	−0.0776578	+	0.440419i
							\(7\)	−6.30582	−	10.9220i	−0.900832	−	1.56029i	−0.826417	−	0.563059i	\(-0.809625\pi\)
−0.0744146	−	0.997227i	\(-0.523709\pi\)
\(11\)	3.30624	−	5.72658i	0.300568	−	0.520598i	−0.675697	−	0.737179i	\(-0.736157\pi\)
							0.976265	+	0.216581i	\(0.0694906\pi\)
\(13\)	−3.66827	+	10.0785i	−0.282175	+	0.775269i	0.714928	+	0.699198i	\(0.246460\pi\)
							−0.997102	+	0.0760703i	\(0.975763\pi\)
\(17\)	5.43966	+	4.56442i	0.319980	+	0.268495i	0.788602	−	0.614903i	\(-0.210805\pi\)
							−0.468622	+	0.883399i	\(0.655249\pi\)
\(19\)	−0.733561	−	18.9858i	−0.0386084	−	0.999254i
							\(23\)	−4.58230	−	25.9875i	−0.199231	−	1.12989i	−0.906264	−	0.422712i	\(-0.861078\pi\)
0.707033	−	0.707180i	\(-0.250033\pi\)
\(29\)	−29.1490	−	34.7385i	−1.00514	−	1.19788i	−0.980164	−	0.198190i	\(-0.936494\pi\)
							−0.0249750	−	0.999688i	\(-0.507951\pi\)
\(31\)	−3.62766	+	2.09443i	−0.117021	+	0.0675622i	−0.557368	−	0.830265i	\(-0.688189\pi\)
							0.440347	+	0.897828i	\(0.354855\pi\)
\(37\)		−	60.0302i		−	1.62244i	−0.584742	−	0.811219i	\(-0.698804\pi\)
							0.584742	−	0.811219i	\(-0.301196\pi\)
\(41\)	23.8321	+	65.4783i	0.581272	+	1.59703i	0.786010	+	0.618214i	\(0.212144\pi\)
							−0.204738	+	0.978817i	\(0.565634\pi\)
\(43\)	−2.04968	+	11.6243i	−0.0476671	+	0.270333i	−0.999321	−	0.0368381i	\(-0.988271\pi\)
							0.951654	+	0.307171i	\(0.0993825\pi\)
\(47\)	−23.8727	+	20.0316i	−0.507931	+	0.426204i	−0.860400	−	0.509619i	\(-0.829786\pi\)
							0.352470	+	0.935823i	\(0.385342\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.3.n.a.41.2	✓	84
19.13	odd	18	inner	95.3.n.a.51.2	yes	84

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.3.n.a.41.2	✓	84	1.1	even	1	trivial
95.3.n.a.51.2	yes	84	19.13	odd	18	inner