Embedded newform 108.2.l.a.95.10

• Label: 108.2.l.a.95.10
• Level: $108$
• Weight: $2$
• Character: 108.95
• Analytic conductor: $0.862$
• Analytic rank: $0$
• Dimension: $96$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.l (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.862384341830\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(16\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.10
Character	\(\chi\)	\(=\)	108.95
Dual form			108.2.l.a.83.10

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.0763531 - 1.41215i) q^{2} +(-0.463152 - 1.66898i) q^{3} +(-1.98834 - 0.215644i) q^{4} +(1.24142 - 1.47946i) q^{5} +(-2.39221 + 0.526609i) q^{6} +(-0.767596 + 2.10895i) q^{7} +(-0.456338 + 2.79137i) q^{8} +(-2.57098 + 1.54598i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\)	\(29\)	\(55\)
\(\chi(n)\)	\(e\left(\frac{17}{18}\right)\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.0763531	−	1.41215i	0.0539898	−	0.998541i
							\(3\)	−0.463152	−	1.66898i	−0.267401	−	0.963585i
\(5\)	1.24142	−	1.47946i	0.555179	−	0.661636i								−0.413340	−	0.910577i	\(-0.635638\pi\)
							0.968519	+	0.248941i	\(0.0800824\pi\)
\(7\)	−0.767596	+	2.10895i	−0.290124	+	0.797109i	0.705924	+	0.708288i	\(0.250532\pi\)
							−0.996048	+	0.0888209i	\(0.971690\pi\)
\(11\)	2.76598	−	2.32094i	0.833975	−	0.699788i	−0.122225	−	0.992502i	\(-0.539003\pi\)
							0.956200	+	0.292714i	\(0.0945584\pi\)
\(13\)	0.799948	−	4.53673i	0.221866	−	1.25826i	−0.646721	−	0.762726i	\(-0.723860\pi\)
							0.868587	−	0.495536i	\(-0.165029\pi\)
\(17\)	3.65512	+	2.11029i	0.886497	+	0.511819i	0.872795	−	0.488087i	\(-0.162305\pi\)
							0.0137019	+	0.999906i	\(0.495638\pi\)
\(19\)	−3.84463	+	2.21970i	−0.882018	+	0.509233i	−0.871323	−	0.490709i	\(-0.836738\pi\)
							−0.0106948	+	0.999943i	\(0.503404\pi\)
\(23\)	4.90294	−	1.78453i	1.02233	−	0.372099i	0.224177	−	0.974548i	\(-0.428031\pi\)
							0.798157	+	0.602449i	\(0.205808\pi\)
\(29\)	0.836409	−	0.147481i	0.155317	−	0.0273866i	−0.0954488	−	0.995434i	\(-0.530429\pi\)
							0.250766	+	0.968048i	\(0.419318\pi\)
\(31\)	0.155947	+	0.428462i	0.0280090	+	0.0769540i	0.952909	−	0.303256i	\(-0.0980738\pi\)
							−0.924900	+	0.380210i	\(0.875852\pi\)
\(37\)	−2.56499	+	4.44270i	−0.421683	+	0.730376i	−0.996104	−	0.0881840i	\(-0.971894\pi\)
							0.574422	+	0.818560i	\(0.305227\pi\)
\(41\)	−11.2302	−	1.98019i	−1.75386	−	0.309254i	−0.797912	−	0.602774i	\(-0.794062\pi\)
							−0.955953	+	0.293521i	\(0.905173\pi\)
\(43\)	6.14371	+	7.32179i	0.936907	+	1.11656i	0.992997	+	0.118136i	\(0.0376920\pi\)
							−0.0560906	+	0.998426i	\(0.517864\pi\)
\(47\)	−6.43838	−	2.34338i	−0.939134	−	0.341817i	−0.173310	−	0.984867i	\(-0.555446\pi\)
							−0.765824	+	0.643050i	\(0.777669\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.l.a.95.10	yes	96
3.2	odd	2		324.2.l.a.71.7		96
4.3	odd	2	inner	108.2.l.a.95.12	yes	96
9.2	odd	6		972.2.l.b.863.15		96
9.4	even	3		972.2.l.d.539.12		96
9.5	odd	6		972.2.l.a.539.5		96
9.7	even	3		972.2.l.c.863.2		96
12.11	even	2		324.2.l.a.71.5		96
27.2	odd	18	inner	108.2.l.a.83.12	yes	96
27.7	even	9		972.2.l.b.107.7		96
27.11	odd	18		972.2.l.d.431.1		96
27.16	even	9		972.2.l.a.431.16		96
27.20	odd	18		972.2.l.c.107.10		96
27.25	even	9		324.2.l.a.251.5		96
36.7	odd	6		972.2.l.c.863.10		96
36.11	even	6		972.2.l.b.863.7		96
36.23	even	6		972.2.l.a.539.16		96
36.31	odd	6		972.2.l.d.539.1		96
108.7	odd	18		972.2.l.b.107.15		96
108.11	even	18		972.2.l.d.431.12		96
108.43	odd	18		972.2.l.a.431.5		96
108.47	even	18		972.2.l.c.107.2		96
108.79	odd	18		324.2.l.a.251.7		96
108.83	even	18	inner	108.2.l.a.83.10	✓	96

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.83.10	✓	96	108.83	even	18	inner
108.2.l.a.83.12	yes	96	27.2	odd	18	inner
108.2.l.a.95.10	yes	96	1.1	even	1	trivial
108.2.l.a.95.12	yes	96	4.3	odd	2	inner
324.2.l.a.71.5		96	12.11	even	2
324.2.l.a.71.7		96	3.2	odd	2
324.2.l.a.251.5		96	27.25	even	9
324.2.l.a.251.7		96	108.79	odd	18
972.2.l.a.431.5		96	108.43	odd	18
972.2.l.a.431.16		96	27.16	even	9
972.2.l.a.539.5		96	9.5	odd	6
972.2.l.a.539.16		96	36.23	even	6
972.2.l.b.107.7		96	27.7	even	9
972.2.l.b.107.15		96	108.7	odd	18
972.2.l.b.863.7		96	36.11	even	6
972.2.l.b.863.15		96	9.2	odd	6
972.2.l.c.107.2		96	108.47	even	18
972.2.l.c.107.10		96	27.20	odd	18
972.2.l.c.863.2		96	9.7	even	3
972.2.l.c.863.10		96	36.7	odd	6
972.2.l.d.431.1		96	27.11	odd	18
972.2.l.d.431.12		96	108.11	even	18
972.2.l.d.539.1		96	36.31	odd	6
972.2.l.d.539.12		96	9.4	even	3