Embedded newform 105.3.v.a.88.3

• Label: 105.3.v.a.88.3
• Level: $105$
• Weight: $3$
• Character: 105.88
• 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			88.3
Character	\(\chi\)	\(=\)	105.88
Dual form			105.3.v.a.37.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.87375 - 0.770020i) q^{2} +(1.67303 - 0.448288i) q^{3} +(4.20143 + 2.42570i) q^{4} +(3.78688 - 3.26489i) q^{5} -5.15308 q^{6} +(-1.65502 + 6.80154i) q^{7} +(-1.79111 - 1.79111i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{5} - 4 q^{7} + 24 q^{8}+O(q^{10}) \)

Character values

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

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.87375	−	0.770020i	−1.43688	−	0.385010i	−0.545438	−	0.838151i	\(-0.683637\pi\)
							−0.891439	+	0.453141i	\(0.850303\pi\)
\(3\)	1.67303	−	0.448288i	0.557678	−	0.149429i
							\(5\)	3.78688	−	3.26489i	0.757376	−	0.652979i
\(7\)	−1.65502	+	6.80154i	−0.236431	+	0.971648i
							\(11\)	6.96127	−	12.0573i	0.632842	−	1.09612i	−0.354126	−	0.935198i	\(-0.615221\pi\)
0.986968	−	0.160917i	\(-0.0514452\pi\)
\(13\)	7.79302	+	7.79302i	0.599463	+	0.599463i	0.940170	−	0.340707i	\(-0.110666\pi\)
							−0.340707	+	0.940170i	\(0.610666\pi\)
\(17\)	−6.92421	−	25.8415i	−0.407307	−	1.52009i	−0.799761	−	0.600318i	\(-0.795041\pi\)
							0.392455	−	0.919771i	\(-0.371626\pi\)
\(19\)	28.5616	−	16.4901i	1.50324	−	0.867898i	0.503251	−	0.864140i	\(-0.332137\pi\)
							0.999993	−	0.00375778i	\(-0.00119614\pi\)
\(23\)	−5.48688	+	20.4773i	−0.238560	+	0.890318i	0.737952	+	0.674854i	\(0.235793\pi\)
							−0.976512	+	0.215464i	\(0.930873\pi\)
\(29\)			18.1531i			0.625971i	0.949758	+	0.312985i	\(0.101329\pi\)
							−0.949758	+	0.312985i	\(0.898671\pi\)
\(31\)	−11.5772	+	20.0522i	−0.373457	+	0.646846i	−0.990095	−	0.140401i	\(-0.955161\pi\)
							0.616638	+	0.787247i	\(0.288494\pi\)
\(37\)	−20.1574	−	5.40117i	−0.544796	−	0.145978i	−0.0240837	−	0.999710i	\(-0.507667\pi\)
							−0.520712	+	0.853732i	\(0.674333\pi\)
\(41\)	−1.69819			−0.0414193			−0.0207097	−	0.999786i	\(-0.506593\pi\)
							−0.0207097	+	0.999786i	\(0.506593\pi\)
\(43\)	26.7992	+	26.7992i	0.623236	+	0.623236i	0.946358	−	0.323121i	\(-0.104732\pi\)
							−0.323121	+	0.946358i	\(0.604732\pi\)
\(47\)	−10.2827	−	2.75524i	−0.218781	−	0.0586222i	0.147763	−	0.989023i	\(-0.452793\pi\)
							−0.366544	+	0.930401i	\(0.619459\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.v.a.88.3	yes	64
3.2	odd	2		315.3.ca.b.298.14		64
5.2	odd	4	inner	105.3.v.a.67.14	yes	64
7.2	even	3	inner	105.3.v.a.58.14	yes	64
15.2	even	4		315.3.ca.b.172.3		64
21.2	odd	6		315.3.ca.b.163.3		64
35.2	odd	12	inner	105.3.v.a.37.3	✓	64
105.2	even	12		315.3.ca.b.37.14		64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.3	✓	64	35.2	odd	12	inner
105.3.v.a.58.14	yes	64	7.2	even	3	inner
105.3.v.a.67.14	yes	64	5.2	odd	4	inner
105.3.v.a.88.3	yes	64	1.1	even	1	trivial
315.3.ca.b.37.14		64	105.2	even	12
315.3.ca.b.163.3		64	21.2	odd	6
315.3.ca.b.172.3		64	15.2	even	4
315.3.ca.b.298.14		64	3.2	odd	2