Embedded newform 105.3.v.a.58.3

• Label: 105.3.v.a.58.3
• Level: $105$
• Weight: $3$
• Character: 105.58
• 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			58.3
Character	\(\chi\)	\(=\)	105.58
Dual form			105.3.v.a.67.3

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

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

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)

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

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.v.a.58.3	yes	64
3.2	odd	2		315.3.ca.b.163.14		64
5.2	odd	4	inner	105.3.v.a.37.14	✓	64
7.4	even	3	inner	105.3.v.a.88.14	yes	64
15.2	even	4		315.3.ca.b.37.3		64
21.11	odd	6		315.3.ca.b.298.3		64
35.32	odd	12	inner	105.3.v.a.67.3	yes	64
105.32	even	12		315.3.ca.b.172.14		64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.14	✓	64	5.2	odd	4	inner
105.3.v.a.58.3	yes	64	1.1	even	1	trivial
105.3.v.a.67.3	yes	64	35.32	odd	12	inner
105.3.v.a.88.14	yes	64	7.4	even	3	inner
315.3.ca.b.37.3		64	15.2	even	4
315.3.ca.b.163.14		64	3.2	odd	2
315.3.ca.b.172.14		64	105.32	even	12
315.3.ca.b.298.3		64	21.11	odd	6