Embedded newform 105.3.t.b.11.5

• Label: 105.3.t.b.11.5
• 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			11.5
Character	\(\chi\)	\(=\)	105.11
Dual form			105.3.t.b.86.5

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.31825 + 1.33844i) q^{2} +(2.46021 - 1.71679i) q^{3} +(1.58287 - 2.74161i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-3.40557 + 7.27281i) q^{6} +(4.89419 + 5.00469i) q^{7} -2.23323i q^{8} +(3.10528 - 8.44732i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 36 q^{4} - 24 q^{6} - 58 q^{7} - 2 q^{9}+O(q^{10}) \)

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	−0.951095	−	0.308900i	\(-0.900039\pi\)
							−0.208032	+	0.978122i	\(0.566706\pi\)
\(3\)	2.46021	−	1.71679i	0.820071	−	0.572262i
							\(5\)	−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	0.996703	−	0.0811419i	\(-0.0258567\pi\)
0.428080	+	0.903741i	\(0.359190\pi\)
\(13\)	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	0.396739	−	0.917931i	\(-0.370142\pi\)
							−0.596582	+	0.802552i	\(0.703475\pi\)
\(19\)	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	−0.618133	−	0.786073i	\(-0.712111\pi\)
							0.371693	+	0.928356i	\(0.378778\pi\)
\(29\)		−	18.8690i		−	0.650654i	−0.945602	−	0.325327i	\(-0.894526\pi\)
							0.945602	−	0.325327i	\(-0.105474\pi\)
\(31\)	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	\(0.156665\pi\)
							−0.881306	+	0.472546i	\(0.843335\pi\)
\(43\)	−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	−0.0978620	−	0.995200i	\(-0.531200\pi\)
							0.812937	+	0.582351i	\(0.197867\pi\)

(See \(a_n\) instead)

Twists

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

    

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