Embedded newform 105.3.o.b.44.13

• Label: 105.3.o.b.44.13
• 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			44.13
Character	\(\chi\)	\(=\)	105.44
Dual form			105.3.o.b.74.13

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.897800 - 1.55504i) q^{2} +(-2.91099 + 0.725349i) q^{3} +(0.387909 + 0.671879i) q^{4} +(3.31295 + 3.74491i) q^{5} +(-1.48554 + 5.17791i) q^{6} +(-1.39571 + 6.85945i) q^{7} +8.57546 q^{8} +(7.94774 - 4.22297i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 44 q^{4} + 80 q^{6} + 12 q^{9}+O(q^{10}) \)

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	−0.549415	−	0.835550i	\(-0.685149\pi\)
							0.998315	+	0.0580320i	\(0.0184826\pi\)
\(3\)	−2.91099	+	0.725349i	−0.970330	+	0.241783i
							\(5\)	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	−0.545110	−	0.838364i	\(-0.683512\pi\)
0.453490	+	0.891262i	\(0.350179\pi\)
\(13\)		−	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	\(0.0179183\pi\)
							−0.450483	+	0.892785i	\(0.648748\pi\)
\(19\)	−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	\(-0.629880\pi\)
							0.993329	−	0.115311i	\(-0.0367865\pi\)
\(29\)		−	52.6691i		−	1.81617i	−0.418781	−	0.908087i	\(-0.637543\pi\)
							0.418781	−	0.908087i	\(-0.362457\pi\)
\(31\)	−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	\(-0.932680\pi\)
							0.977719	−	0.209918i	\(-0.0673195\pi\)
\(43\)			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	−0.619226	−	0.785213i	\(-0.712553\pi\)
							0.989627	+	0.143659i	\(0.0458868\pi\)

(See \(a_n\) instead)

Twists

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

    

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