Embedded newform 105.3.w.a.17.19

• Label: 105.3.w.a.17.19
• Level: $105$
• Weight: $3$
• Character: 105.17
• Analytic conductor: $2.861$
• Analytic rank: $0$
• Dimension: $112$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.w (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.86104277578\)
Analytic rank:	\(0\)
Dimension:	\(112\)
Relative dimension:	\(28\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.19
Character	\(\chi\)	\(=\)	105.17
Dual form			105.3.w.a.68.19

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.40147 + 0.375522i) q^{2} +(0.0184202 + 2.99994i) q^{3} +(-1.64101 - 0.947435i) q^{4} +(3.73472 + 3.32444i) q^{5} +(-1.10073 + 4.21124i) q^{6} +(2.97299 + 6.33730i) q^{7} +(-6.04782 - 6.04782i) q^{8} +(-8.99932 + 0.110519i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 6 q^{3} - 16 q^{7}+O(q^{10}) \)

Character values

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

\(n\)	\(22\)	\(31\)	\(71\)
\(\chi(n)\)	\(e\left(\frac{1}{4}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.40147	+	0.375522i	0.700734	+	0.187761i	0.591559	−	0.806261i	\(-0.298513\pi\)
							0.109175	+	0.994023i	\(0.465179\pi\)
\(3\)	0.0184202	+	2.99994i	0.00614008	+	0.999981i
							\(5\)	3.73472	+	3.32444i	0.746943	+	0.664888i
\(7\)	2.97299	+	6.33730i	0.424712	+	0.905328i
							\(11\)	3.76549	+	2.17401i	0.342318	+	0.197637i	0.661296	−	0.750125i	\(-0.270007\pi\)
−0.318979	+	0.947762i	\(0.603340\pi\)
\(13\)	4.76059	+	4.76059i	0.366199	+	0.366199i	0.866089	−	0.499890i	\(-0.166626\pi\)
							−0.499890	+	0.866089i	\(0.666626\pi\)
\(17\)	19.0658	−	5.10867i	1.12152	−	0.300510i	0.350021	−	0.936742i	\(-0.386174\pi\)
							0.771498	+	0.636231i	\(0.219508\pi\)
\(19\)	−12.5949	−	21.8150i	−0.662890	−	1.14816i	−0.979853	−	0.199721i	\(-0.935996\pi\)
							0.316963	−	0.948438i	\(-0.397337\pi\)
\(23\)	8.21961	−	30.6760i	0.357374	−	1.33374i	−0.520095	−	0.854108i	\(-0.674104\pi\)
							0.877470	−	0.479632i	\(-0.159230\pi\)
\(29\)	28.8306			0.994158			0.497079	−	0.867705i	\(-0.334406\pi\)
							0.497079	+	0.867705i	\(0.334406\pi\)
\(31\)	−12.3444	−	7.12704i	−0.398206	−	0.229904i	0.287504	−	0.957780i	\(-0.407175\pi\)
							−0.685710	+	0.727875i	\(0.740508\pi\)
\(37\)	13.1470	−	49.0654i	0.355325	−	1.32609i	−0.524750	−	0.851257i	\(-0.675841\pi\)
							0.880075	−	0.474835i	\(-0.157492\pi\)
\(41\)	−1.56196			−0.0380967			−0.0190483	−	0.999819i	\(-0.506064\pi\)
							−0.0190483	+	0.999819i	\(0.506064\pi\)
\(43\)	−46.2033	+	46.2033i	−1.07449	+	1.07449i	−0.0775021	+	0.996992i	\(0.524694\pi\)
							−0.996992	+	0.0775021i	\(0.975306\pi\)
\(47\)	3.56182	−	13.2929i	0.0757834	−	0.282828i	−0.917626	−	0.397444i	\(-0.869897\pi\)
							0.993410	+	0.114616i	\(0.0365639\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.w.a.17.19	yes	112
3.2	odd	2	inner	105.3.w.a.17.10	✓	112
5.3	odd	4	inner	105.3.w.a.38.19	yes	112
7.5	odd	6	inner	105.3.w.a.47.10	yes	112
15.8	even	4	inner	105.3.w.a.38.10	yes	112
21.5	even	6	inner	105.3.w.a.47.19	yes	112
35.33	even	12	inner	105.3.w.a.68.10	yes	112
105.68	odd	12	inner	105.3.w.a.68.19	yes	112

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.10	✓	112	3.2	odd	2	inner
105.3.w.a.17.19	yes	112	1.1	even	1	trivial
105.3.w.a.38.10	yes	112	15.8	even	4	inner
105.3.w.a.38.19	yes	112	5.3	odd	4	inner
105.3.w.a.47.10	yes	112	7.5	odd	6	inner
105.3.w.a.47.19	yes	112	21.5	even	6	inner
105.3.w.a.68.10	yes	112	35.33	even	12	inner
105.3.w.a.68.19	yes	112	105.68	odd	12	inner