Embedded newform 105.4.s.b.26.2

• Label: 105.4.s.b.26.2
• Level: $105$
• Weight: $4$
• Character: 105.26
• Analytic conductor: $6.195$
• Analytic rank: $0$
• Dimension: $32$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.19520055060\)
Analytic rank:	\(0\)
Dimension:	\(32\)
Relative dimension:	\(16\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.2
Character	\(\chi\)	\(=\)	105.26
Dual form			105.4.s.b.101.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-3.95258 - 2.28202i) q^{2} +(-1.04959 - 5.08904i) q^{3} +(6.41528 + 11.1116i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-7.46472 + 22.5101i) q^{6} +(-15.3726 - 10.3287i) q^{7} -22.0469i q^{8} +(-24.7967 + 10.6828i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 64 q^{4} + 80 q^{5} + 28 q^{6} + 46 q^{7} - 98 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(22\)	\(31\)	\(71\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−3.95258	−	2.28202i	−1.39745	−	0.806818i	−0.403324	−	0.915057i	\(-0.632145\pi\)
							−0.994125	+	0.108239i	\(0.965479\pi\)
\(3\)	−1.04959	−	5.08904i	−0.201994	−	0.979387i
							\(5\)	2.50000	−	4.33013i	0.223607	−	0.387298i
\(7\)	−15.3726	−	10.3287i	−0.830043	−	0.557699i
							\(11\)	−38.8392	+	22.4238i	−1.06459	+	0.614640i	−0.926698	−	0.375807i	\(-0.877366\pi\)
−0.137890	+	0.990447i	\(0.544032\pi\)
\(13\)		−	21.9561i		−	0.468426i	−0.972185	−	0.234213i	\(-0.924749\pi\)
							0.972185	−	0.234213i	\(-0.0752513\pi\)
\(17\)	18.3222	+	31.7351i	0.261400	+	0.452758i	0.966614	−	0.256236i	\(-0.0824825\pi\)
							−0.705214	+	0.708994i	\(0.749149\pi\)
\(19\)	91.7755	+	52.9866i	1.10814	+	0.639788i	0.938348	−	0.345692i	\(-0.112356\pi\)
							0.169796	+	0.985479i	\(0.445689\pi\)
\(23\)	21.5307	+	12.4308i	0.195194	+	0.112695i	0.594412	−	0.804161i	\(-0.297385\pi\)
							−0.399218	+	0.916856i	\(0.630718\pi\)
\(29\)		−	31.6068i		−	0.202387i	−0.994867	−	0.101194i	\(-0.967734\pi\)
							0.994867	−	0.101194i	\(-0.0322662\pi\)
\(31\)	−262.288	+	151.432i	−1.51962	+	0.877356i	−0.519892	+	0.854232i	\(0.674028\pi\)
							−0.999733	+	0.0231240i	\(0.992639\pi\)
\(37\)	130.913	−	226.748i	0.581674	−	1.00749i	−0.413607	−	0.910456i	\(-0.635731\pi\)
							0.995281	−	0.0970336i	\(-0.0309354\pi\)
\(41\)	294.707			1.12257			0.561287	−	0.827621i	\(-0.310307\pi\)
							0.561287	+	0.827621i	\(0.310307\pi\)
\(43\)	−302.029			−1.07114			−0.535570	−	0.844491i	\(-0.679903\pi\)
							−0.535570	+	0.844491i	\(0.679903\pi\)
\(47\)	−59.6172	+	103.260i	−0.185023	+	0.320468i	−0.943584	−	0.331133i	\(-0.892569\pi\)
							0.758562	+	0.651601i	\(0.225902\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.s.b.26.2	yes	32
3.2	odd	2		105.4.s.a.26.15	✓	32
7.3	odd	6		105.4.s.a.101.15	yes	32
21.17	even	6	inner	105.4.s.b.101.2	yes	32

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.s.a.26.15	✓	32	3.2	odd	2
105.4.s.a.101.15	yes	32	7.3	odd	6
105.4.s.b.26.2	yes	32	1.1	even	1	trivial
105.4.s.b.101.2	yes	32	21.17	even	6	inner