Embedded newform 105.4.s.b.26.6

• Label: 105.4.s.b.26.6
• Level: $105$
• Weight: $4$
• Character: 105.26
• Analytic conductor: $6.195$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.19520055060\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.6
Character	\(\chi\)	\(=\)	105.26
Dual form			105.4.s.b.101.6

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.48940 - 0.859905i) q^{2} +(-4.80226 + 1.98451i) q^{3} +(-2.52113 - 4.36672i) q^{4} +(2.50000 - 4.33013i) q^{5} +(8.85898 + 1.17376i) q^{6} +(2.28179 - 18.3792i) q^{7} +22.4302i q^{8} +(19.1235 - 19.0603i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 64 q^{4} + 80 q^{5} + 28 q^{6} + 46 q^{7} - 98 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\)	\(22\)	\(31\)	\(71\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.48940	−	0.859905i	−0.526582	−	0.304022i	0.213041	−	0.977043i	\(-0.431663\pi\)
							−0.739624	+	0.673021i	\(0.764996\pi\)
\(3\)	−4.80226	+	1.98451i	−0.924196	+	0.381919i
							\(5\)	2.50000	−	4.33013i	0.223607	−	0.387298i
\(7\)	2.28179	−	18.3792i	0.123205	−	0.992381i
							\(11\)	−49.7733	+	28.7366i	−1.36429	+	0.787674i	−0.990192	−	0.139714i	\(-0.955382\pi\)
−0.374100	+	0.927388i	\(0.622048\pi\)
\(13\)			44.6643i			0.952896i	0.879203	+	0.476448i	\(0.158076\pi\)
							−0.879203	+	0.476448i	\(0.841924\pi\)
\(17\)	54.8920	+	95.0758i	0.783134	+	1.35643i	0.930108	+	0.367287i	\(0.119713\pi\)
							−0.146974	+	0.989140i	\(0.546953\pi\)
\(19\)	−79.5306	−	45.9170i	−0.960293	−	0.554426i	−0.0640300	−	0.997948i	\(-0.520395\pi\)
							−0.896263	+	0.443522i	\(0.853729\pi\)
\(23\)	27.1329	+	15.6652i	0.245983	+	0.142018i	0.617923	−	0.786238i	\(-0.287974\pi\)
							−0.371941	+	0.928257i	\(0.621307\pi\)
\(29\)			183.561i			1.17539i	0.809082	+	0.587696i	\(0.199965\pi\)
							−0.809082	+	0.587696i	\(0.800035\pi\)
\(31\)	123.493	−	71.2990i	0.715486	−	0.413086i	−0.0976027	−	0.995225i	\(-0.531117\pi\)
							0.813089	+	0.582139i	\(0.197784\pi\)
\(37\)	−114.912	+	199.033i	−0.510579	+	0.884349i	0.489346	+	0.872090i	\(0.337236\pi\)
							−0.999925	+	0.0122589i	\(0.996098\pi\)
\(41\)	−185.753			−0.707555			−0.353778	−	0.935330i	\(-0.615103\pi\)
							−0.353778	+	0.935330i	\(0.615103\pi\)
\(43\)	−22.3617			−0.0793054			−0.0396527	−	0.999214i	\(-0.512625\pi\)
							−0.0396527	+	0.999214i	\(0.512625\pi\)
\(47\)	116.516	−	201.811i	0.361608	−	0.626323i	−0.626618	−	0.779326i	\(-0.715561\pi\)
							0.988226	+	0.153004i	\(0.0488947\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.s.b.26.6	yes	32
3.2	odd	2		105.4.s.a.26.11	✓	32
7.3	odd	6		105.4.s.a.101.11	yes	32
21.17	even	6	inner	105.4.s.b.101.6	yes	32

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.s.a.26.11	✓	32	3.2	odd	2
105.4.s.a.101.11	yes	32	7.3	odd	6
105.4.s.b.26.6	yes	32	1.1	even	1	trivial
105.4.s.b.101.6	yes	32	21.17	even	6	inner