Embedded newform 105.3.o.b.44.7

• Label: 105.3.o.b.44.7
• Level: $105$
• Weight: $3$
• Character: 105.44
• 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			44.7
Character	\(\chi\)	\(=\)	105.44
Dual form			105.3.o.b.74.7

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.897800 + 1.55504i) q^{2} +(-2.08367 + 2.15832i) q^{3} +(0.387909 + 0.671879i) q^{4} +(-3.31295 - 3.74491i) q^{5} +(-1.48554 - 5.17791i) q^{6} +(-1.39571 + 6.85945i) q^{7} -8.57546 q^{8} +(-0.316668 - 8.99443i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 44 q^{4} + 80 q^{6} + 12 q^{9}+O(q^{10}) \)

Character values

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

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.897800	+	1.55504i	−0.448900	+	0.777518i	−0.998315	−	0.0580320i	\(-0.981517\pi\)
							0.549415	+	0.835550i	\(0.314851\pi\)
\(3\)	−2.08367	+	2.15832i	−0.694556	+	0.719439i
							\(5\)	−3.31295	−	3.74491i	−0.662590	−	0.748983i
\(7\)	−1.39571	+	6.85945i	−0.199386	+	0.979921i
							\(11\)	1.00783	−	0.581870i	0.0916208	−	0.0528973i	−0.453490	−	0.891262i	\(-0.649821\pi\)
0.545110	+	0.838364i	\(0.316488\pi\)
\(13\)		−	12.4799i		−	0.959993i	−0.877270	−	0.479996i	\(-0.840638\pi\)
							0.877270	−	0.479996i	\(-0.159362\pi\)
\(17\)	−9.31485	−	16.1338i	−0.547933	−	0.949047i	−0.998416	−	0.0562623i	\(-0.982082\pi\)
							0.450483	−	0.892785i	\(-0.351252\pi\)
\(19\)	−15.2033	+	26.3329i	−0.800174	+	1.38594i	0.119327	+	0.992855i	\(0.461926\pi\)
							−0.919501	+	0.393087i	\(0.871407\pi\)
\(23\)	−13.7201	+	23.7640i	−0.596527	+	1.03322i	0.396802	+	0.917904i	\(0.370120\pi\)
							−0.993329	+	0.115311i	\(0.963213\pi\)
\(29\)			52.6691i			1.81617i	0.418781	+	0.908087i	\(0.362457\pi\)
							−0.418781	+	0.908087i	\(0.637543\pi\)
\(31\)	−17.2838	−	29.9364i	−0.557542	−	0.965692i	−0.997701	−	0.0677718i	\(-0.978411\pi\)
							0.440158	−	0.897920i	\(-0.354922\pi\)
\(37\)	0.357210	+	0.206235i	0.00965431	+	0.00557392i	0.504819	−	0.863225i	\(-0.331559\pi\)
							−0.495165	+	0.868799i	\(0.664892\pi\)
\(41\)			17.2132i			0.419835i	0.977719	+	0.209918i	\(0.0673195\pi\)
							−0.977719	+	0.209918i	\(0.932680\pi\)
\(43\)			7.86972i			0.183017i	0.995804	+	0.0915084i	\(0.0291688\pi\)
							−0.995804	+	0.0915084i	\(0.970831\pi\)
\(47\)	−17.4089	+	30.1530i	−0.370401	+	0.641554i	−0.989627	−	0.143659i	\(-0.954113\pi\)
							0.619226	+	0.785213i	\(0.287447\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.o.b.44.7	✓	40
3.2	odd	2	inner	105.3.o.b.44.13	yes	40
5.4	even	2	inner	105.3.o.b.44.14	yes	40
7.4	even	3	inner	105.3.o.b.74.8	yes	40
15.14	odd	2	inner	105.3.o.b.44.8	yes	40
21.11	odd	6	inner	105.3.o.b.74.14	yes	40
35.4	even	6	inner	105.3.o.b.74.13	yes	40
105.74	odd	6	inner	105.3.o.b.74.7	yes	40

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.o.b.44.7	✓	40	1.1	even	1	trivial
105.3.o.b.44.8	yes	40	15.14	odd	2	inner
105.3.o.b.44.13	yes	40	3.2	odd	2	inner
105.3.o.b.44.14	yes	40	5.4	even	2	inner
105.3.o.b.74.7	yes	40	105.74	odd	6	inner
105.3.o.b.74.8	yes	40	7.4	even	3	inner
105.3.o.b.74.13	yes	40	35.4	even	6	inner
105.3.o.b.74.14	yes	40	21.11	odd	6	inner