Embedded newform 105.3.t.b.11.14

• Label: 105.3.t.b.11.14
• Level: $105$
• Weight: $3$
• Character: 105.11
• Analytic conductor: $2.861$
• Analytic rank: $0$
• Dimension: $36$
• CM: no
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(2.86104277578\)
Analytic rank:	\(0\)
Dimension:	\(36\)
Relative dimension:	\(18\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.14
Character	\(\chi\)	\(=\)	105.11
Dual form			105.3.t.b.86.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(2.31825 - 1.33844i) q^{2} +(0.256676 - 2.98900i) q^{3} +(1.58287 - 2.74161i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-3.40557 - 7.27281i) q^{6} +(4.89419 + 5.00469i) q^{7} +2.23323i q^{8} +(-8.86824 - 1.53441i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 36 q^{4} - 24 q^{6} - 58 q^{7} - 2 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(22\)	\(31\)	\(71\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	2.31825	−	1.33844i	1.15913	−	0.669222i	0.208032	−	0.978122i	\(-0.433294\pi\)
							0.951095	+	0.308900i	\(0.0999607\pi\)
\(3\)	0.256676	−	2.98900i	0.0855585	−	0.996333i
							\(5\)	1.93649	−	1.11803i	0.387298	−	0.223607i
\(7\)	4.89419	+	5.00469i	0.699170	+	0.714956i
							\(11\)	−15.6726	−	9.04859i	−1.42478	−	0.822599i	−0.428080	−	0.903741i	\(-0.640810\pi\)
−0.996703	+	0.0811419i	\(0.974143\pi\)
\(13\)	2.70603			0.208156			0.104078	−	0.994569i	\(-0.466811\pi\)
							0.104078	+	0.994569i	\(0.466811\pi\)
\(17\)	3.39734	+	1.96145i	0.199843	+	0.115380i	0.596582	−	0.802552i	\(-0.296525\pi\)
							−0.396739	+	0.917931i	\(0.629858\pi\)
\(19\)	14.7810	+	25.6015i	0.777948	+	1.34745i	0.933122	+	0.359559i	\(0.117073\pi\)
							−0.155174	+	0.987887i	\(0.549594\pi\)
\(23\)	5.66814	−	3.27250i	0.246441	−	0.142283i	−0.371693	−	0.928356i	\(-0.621222\pi\)
							0.618133	+	0.786073i	\(0.287889\pi\)
\(29\)			18.8690i			0.650654i	0.945602	+	0.325327i	\(0.105474\pi\)
							−0.945602	+	0.325327i	\(0.894526\pi\)
\(31\)	12.6486	−	21.9079i	0.408018	−	0.706708i	−0.586650	−	0.809841i	\(-0.699553\pi\)
							0.994668	+	0.103133i	\(0.0328867\pi\)
\(37\)	−33.5038	−	58.0303i	−0.905509	−	1.56839i	−0.820232	−	0.572031i	\(-0.806156\pi\)
							−0.0852768	−	0.996357i	\(-0.527177\pi\)
\(41\)		−	38.7488i		−	0.945092i	−0.881306	−	0.472546i	\(-0.843335\pi\)
							0.881306	−	0.472546i	\(-0.156665\pi\)
\(43\)	−63.9074			−1.48622			−0.743109	−	0.669171i	\(-0.766650\pi\)
							−0.743109	+	0.669171i	\(0.766650\pi\)
\(47\)	−33.6085	+	19.4039i	−0.715075	+	0.412849i	−0.812937	−	0.582351i	\(-0.802133\pi\)
							0.0978620	+	0.995200i	\(0.468800\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.t.b.11.14	yes	36
3.2	odd	2	inner	105.3.t.b.11.5	✓	36
7.2	even	3	inner	105.3.t.b.86.5	yes	36
21.2	odd	6	inner	105.3.t.b.86.14	yes	36

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.t.b.11.5	✓	36	3.2	odd	2	inner
105.3.t.b.11.14	yes	36	1.1	even	1	trivial
105.3.t.b.86.5	yes	36	7.2	even	3	inner
105.3.t.b.86.14	yes	36	21.2	odd	6	inner