Embedded newform 105.3.o.b.74.7

• Label: 105.3.o.b.74.7
• 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			74.7
Character	\(\chi\)	\(=\)	105.74
Dual form			105.3.o.b.44.7

$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\)	\(22\)	\(31\)	\(71\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.897800	−	1.55504i	−0.448900	−	0.777518i	0.549415	−	0.835550i	\(-0.314851\pi\)
							−0.998315	+	0.0580320i	\(0.981517\pi\)
\(3\)	−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	0.545110	−	0.838364i	\(-0.316488\pi\)
−0.453490	+	0.891262i	\(0.649821\pi\)
\(13\)			12.4799i			0.959993i	0.877270	+	0.479996i	\(0.159362\pi\)
							−0.877270	+	0.479996i	\(0.840638\pi\)
\(17\)	−9.31485	+	16.1338i	−0.547933	+	0.949047i	0.450483	+	0.892785i	\(0.351252\pi\)
							−0.998416	+	0.0562623i	\(0.982082\pi\)
\(19\)	−15.2033	−	26.3329i	−0.800174	−	1.38594i	−0.919501	−	0.393087i	\(-0.871407\pi\)
							0.119327	−	0.992855i	\(-0.461926\pi\)
\(23\)	−13.7201	−	23.7640i	−0.596527	−	1.03322i	−0.993329	−	0.115311i	\(-0.963213\pi\)
							0.396802	−	0.917904i	\(-0.370120\pi\)
\(29\)		−	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	0.440158	+	0.897920i	\(0.354922\pi\)
							−0.997701	+	0.0677718i	\(0.978411\pi\)
\(37\)	0.357210	−	0.206235i	0.00965431	−	0.00557392i	−0.495165	−	0.868799i	\(-0.664892\pi\)
							0.504819	+	0.863225i	\(0.331559\pi\)
\(41\)		−	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	\(-0.970831\pi\)
							0.995804	−	0.0915084i	\(-0.0291688\pi\)
\(47\)	−17.4089	−	30.1530i	−0.370401	−	0.641554i	0.619226	−	0.785213i	\(-0.287447\pi\)
							−0.989627	+	0.143659i	\(0.954113\pi\)

(See \(a_n\) instead)

Twists

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

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.o.b.44.7	✓	40	105.44	odd	6	inner
105.3.o.b.44.8	yes	40	7.2	even	3	inner
105.3.o.b.44.13	yes	40	35.9	even	6	inner
105.3.o.b.44.14	yes	40	21.2	odd	6	inner
105.3.o.b.74.7	yes	40	1.1	even	1	trivial
105.3.o.b.74.8	yes	40	15.14	odd	2	inner
105.3.o.b.74.13	yes	40	3.2	odd	2	inner
105.3.o.b.74.14	yes	40	5.4	even	2	inner