Embedded newform 105.3.v.a.67.3

• Label: 105.3.v.a.67.3
• Level: $105$
• Weight: $3$
• Character: 105.67
• Analytic conductor: $2.861$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.v (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.86104277578\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(16\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.3
Character	\(\chi\)	\(=\)	105.67
Dual form			105.3.v.a.58.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.773463 + 2.88660i) q^{2} +(0.448288 + 1.67303i) q^{3} +(-4.27013 - 2.46536i) q^{4} +(4.24741 + 2.63808i) q^{5} -5.17611 q^{6} +(-4.68804 + 5.19830i) q^{7} +(1.96674 - 1.96674i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{5} - 4 q^{7} + 24 q^{8}+O(q^{10}) \)

Character values

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

\(n\)	\(22\)	\(31\)	\(71\)
\(\chi(n)\)	\(e\left(\frac{1}{4}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.773463	+	2.88660i	−0.386731	+	1.44330i	0.448688	+	0.893688i	\(0.351891\pi\)
							−0.835419	+	0.549613i	\(0.814775\pi\)
\(3\)	0.448288	+	1.67303i	0.149429	+	0.557678i
							\(5\)	4.24741	+	2.63808i	0.849483	+	0.527616i
\(7\)	−4.68804	+	5.19830i	−0.669719	+	0.742614i
							\(11\)	6.71313	−	11.6275i	0.610285	−	1.05704i	−0.380907	−	0.924613i	\(-0.624388\pi\)
0.991192	−	0.132431i	\(-0.0422784\pi\)
\(13\)	−3.94411	+	3.94411i	−0.303393	+	0.303393i	−0.842340	−	0.538947i	\(-0.818822\pi\)
							0.538947	+	0.842340i	\(0.318822\pi\)
\(17\)	9.46609	−	2.53643i	0.556829	−	0.149202i	0.0305799	−	0.999532i	\(-0.490265\pi\)
							0.526249	+	0.850330i	\(0.323598\pi\)
\(19\)	4.57992	−	2.64422i	0.241049	−	0.139169i	−0.374610	−	0.927182i	\(-0.622223\pi\)
							0.615659	+	0.788013i	\(0.288890\pi\)
\(23\)	7.39285	+	1.98091i	0.321428	+	0.0861264i	0.415925	−	0.909399i	\(-0.363458\pi\)
							−0.0944974	+	0.995525i	\(0.530124\pi\)
\(29\)			36.7188i			1.26616i	0.774085	+	0.633082i	\(0.218211\pi\)
							−0.774085	+	0.633082i	\(0.781789\pi\)
\(31\)	−9.71723	+	16.8307i	−0.313459	+	0.542927i	−0.979109	−	0.203337i	\(-0.934821\pi\)
							0.665650	+	0.746264i	\(0.268155\pi\)
\(37\)	−11.7317	+	43.7832i	−0.317072	+	1.18333i	0.604973	+	0.796246i	\(0.293184\pi\)
							−0.922045	+	0.387083i	\(0.873483\pi\)
\(41\)	57.9301			1.41293			0.706464	−	0.707749i	\(-0.250289\pi\)
							0.706464	+	0.707749i	\(0.250289\pi\)
\(43\)	46.3359	−	46.3359i	1.07758	−	1.07758i	0.0808525	−	0.996726i	\(-0.474236\pi\)
							0.996726	−	0.0808525i	\(-0.0257643\pi\)
\(47\)	16.4446	−	61.3721i	0.349885	−	1.30579i	−0.536915	−	0.843636i	\(-0.680410\pi\)
							0.886800	−	0.462153i	\(-0.152923\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.v.a.67.3	yes	64
3.2	odd	2		315.3.ca.b.172.14		64
5.3	odd	4	inner	105.3.v.a.88.14	yes	64
7.2	even	3	inner	105.3.v.a.37.14	✓	64
15.8	even	4		315.3.ca.b.298.3		64
21.2	odd	6		315.3.ca.b.37.3		64
35.23	odd	12	inner	105.3.v.a.58.3	yes	64
105.23	even	12		315.3.ca.b.163.14		64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.14	✓	64	7.2	even	3	inner
105.3.v.a.58.3	yes	64	35.23	odd	12	inner
105.3.v.a.67.3	yes	64	1.1	even	1	trivial
105.3.v.a.88.14	yes	64	5.3	odd	4	inner
315.3.ca.b.37.3		64	21.2	odd	6
315.3.ca.b.163.14		64	105.23	even	12
315.3.ca.b.172.14		64	3.2	odd	2
315.3.ca.b.298.3		64	15.8	even	4