Embedded newform 105.3.o.b.74.4

• Label: 105.3.o.b.74.4
• Level: $105$
• Weight: $3$
• Character: 105.74
• Analytic conductor: $2.861$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $8$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(2.86104277578\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(20\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			74.4
Character	\(\chi\)	\(=\)	105.74
Dual form			105.3.o.b.44.4

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.60486 - 2.77971i) q^{2} +(0.199928 + 2.99333i) q^{3} +(-3.15118 + 5.45800i) q^{4} +(1.12712 - 4.87130i) q^{5} +(7.99972 - 5.35963i) q^{6} +(-6.02754 - 3.55932i) q^{7} +7.38994 q^{8} +(-8.92006 + 1.19690i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 44 q^{4} + 80 q^{6} + 12 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.60486	−	2.77971i	−0.802432	−	1.38985i	−0.918011	−	0.396555i	\(-0.870206\pi\)
							0.115579	−	0.993298i	\(-0.463128\pi\)
\(3\)	0.199928	+	2.99333i	0.0666427	+	0.997777i
							\(5\)	1.12712	−	4.87130i	0.225423	−	0.974261i
\(7\)	−6.02754	−	3.55932i	−0.861077	−	0.508474i
							\(11\)	−10.5523	−	6.09236i	−0.959298	−	0.553851i	−0.0633411	−	0.997992i	\(-0.520176\pi\)
−0.895957	+	0.444141i	\(0.853509\pi\)
\(13\)		−	8.47270i		−	0.651746i	−0.945414	−	0.325873i	\(-0.894342\pi\)
							0.945414	−	0.325873i	\(-0.105658\pi\)
\(17\)	−5.29476	+	9.17080i	−0.311457	+	0.539459i	−0.978678	−	0.205401i	\(-0.934150\pi\)
							0.667221	+	0.744859i	\(0.267484\pi\)
\(19\)	−10.0823	−	17.4631i	−0.530649	−	0.919111i	−0.999360	−	0.0357599i	\(-0.988615\pi\)
							0.468711	−	0.883351i	\(-0.344718\pi\)
\(23\)	15.2706	+	26.4494i	0.663939	+	1.14998i	0.979572	+	0.201094i	\(0.0644497\pi\)
							−0.315633	+	0.948881i	\(0.602217\pi\)
\(29\)		−	42.8910i		−	1.47900i	−0.673157	−	0.739499i	\(-0.735062\pi\)
							0.673157	−	0.739499i	\(-0.264938\pi\)
\(31\)	−6.11033	+	10.5834i	−0.197107	+	0.341400i	−0.947589	−	0.319491i	\(-0.896488\pi\)
							0.750482	+	0.660891i	\(0.229821\pi\)
\(37\)	28.8063	−	16.6313i	0.778550	−	0.449496i	−0.0573663	−	0.998353i	\(-0.518270\pi\)
							0.835916	+	0.548857i	\(0.184937\pi\)
\(41\)		−	6.40934i		−	0.156325i	−0.996941	−	0.0781627i	\(-0.975095\pi\)
							0.996941	−	0.0781627i	\(-0.0249054\pi\)
\(43\)			20.0231i			0.465653i	0.972518	+	0.232827i	\(0.0747975\pi\)
							−0.972518	+	0.232827i	\(0.925203\pi\)
\(47\)	11.8740	+	20.5664i	0.252639	+	0.437583i	0.964251	−	0.264989i	\(-0.0853683\pi\)
							−0.711613	+	0.702572i	\(0.752035\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.o.b.74.4	yes	40
3.2	odd	2	inner	105.3.o.b.74.18	yes	40
5.4	even	2	inner	105.3.o.b.74.17	yes	40
7.2	even	3	inner	105.3.o.b.44.3	✓	40
15.14	odd	2	inner	105.3.o.b.74.3	yes	40
21.2	odd	6	inner	105.3.o.b.44.17	yes	40
35.9	even	6	inner	105.3.o.b.44.18	yes	40
105.44	odd	6	inner	105.3.o.b.44.4	yes	40

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.o.b.44.3	✓	40	7.2	even	3	inner
105.3.o.b.44.4	yes	40	105.44	odd	6	inner
105.3.o.b.44.17	yes	40	21.2	odd	6	inner
105.3.o.b.44.18	yes	40	35.9	even	6	inner
105.3.o.b.74.3	yes	40	15.14	odd	2	inner
105.3.o.b.74.4	yes	40	1.1	even	1	trivial
105.3.o.b.74.17	yes	40	5.4	even	2	inner
105.3.o.b.74.18	yes	40	3.2	odd	2	inner