Newform orbit 1932.2.u.a

• Label: 1932.2.u.a
• Level: $1932$
• Weight: $2$
• Character orbit: 1932.u
• Analytic conductor: $15.427$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1932.u (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(15.4270976705\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 64 q + 32 q^{9}+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
229.1		0		−0.866025	+	0.500000i		0		−1.45500	+	2.52013i		0		−0.753219	+	2.53627i		0		0.500000	−	0.866025i		0
229.2		0		−0.866025	+	0.500000i		0		1.45500	−	2.52013i		0		0.753219	−	2.53627i		0		0.500000	−	0.866025i		0
229.3		0		−0.866025	+	0.500000i		0		−1.40447	+	2.43261i		0		−2.62121	−	0.359489i		0		0.500000	−	0.866025i		0
229.4		0		−0.866025	+	0.500000i		0		1.40447	−	2.43261i		0		2.62121	+	0.359489i		0		0.500000	−	0.866025i		0
229.5		0		−0.866025	+	0.500000i		0		−1.17373	+	2.03296i		0		1.92869	−	1.81112i		0		0.500000	−	0.866025i		0
229.6		0		−0.866025	+	0.500000i		0		1.17373	−	2.03296i		0		−1.92869	+	1.81112i		0		0.500000	−	0.866025i		0
229.7		0		−0.866025	+	0.500000i		0		−0.791250	+	1.37049i		0		2.62506	−	0.330238i		0		0.500000	−	0.866025i		0
229.8		0		−0.866025	+	0.500000i		0		0.791250	−	1.37049i		0		−2.62506	+	0.330238i		0		0.500000	−	0.866025i		0
229.9		0		−0.866025	+	0.500000i		0		−0.559957	+	0.969874i		0		−0.172696	−	2.64011i		0		0.500000	−	0.866025i		0
229.10		0		−0.866025	+	0.500000i		0		0.559957	−	0.969874i		0		0.172696	+	2.64011i		0		0.500000	−	0.866025i		0
229.11		0		−0.866025	+	0.500000i		0		−0.446977	+	0.774187i		0		−0.103193	+	2.64374i		0		0.500000	−	0.866025i		0
229.12		0		−0.866025	+	0.500000i		0		0.446977	−	0.774187i		0		0.103193	−	2.64374i		0		0.500000	−	0.866025i		0
229.13		0		−0.866025	+	0.500000i		0		−1.65918	+	2.87378i		0		−2.30661	−	1.29598i		0		0.500000	−	0.866025i		0
229.14		0		−0.866025	+	0.500000i		0		1.65918	−	2.87378i		0		2.30661	+	1.29598i		0		0.500000	−	0.866025i		0
229.15		0		−0.866025	+	0.500000i		0		−2.03041	+	3.51678i		0		0.701513	+	2.55105i		0		0.500000	−	0.866025i		0
229.16		0		−0.866025	+	0.500000i		0		2.03041	−	3.51678i		0		−0.701513	−	2.55105i		0		0.500000	−	0.866025i		0
229.17		0		0.866025	−	0.500000i		0		−1.66862	+	2.89014i		0		1.72804	+	2.00347i		0		0.500000	−	0.866025i		0
229.18		0		0.866025	−	0.500000i		0		1.66862	−	2.89014i		0		−1.72804	−	2.00347i		0		0.500000	−	0.866025i		0
229.19		0		0.866025	−	0.500000i		0		−1.60867	+	2.78629i		0		−2.04215	+	1.68215i		0		0.500000	−	0.866025i		0
229.20		0		0.866025	−	0.500000i		0		1.60867	−	2.78629i		0		2.04215	−	1.68215i		0		0.500000	−	0.866025i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.d	odd	6	1	inner
23.b	odd	2	1	inner
161.g	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1932.2.u.a	✓	64
7.d	odd	6	1	inner	1932.2.u.a	✓	64
23.b	odd	2	1	inner	1932.2.u.a	✓	64
161.g	even	6	1	inner	1932.2.u.a	✓	64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1932.2.u.a	✓	64	1.a	even	1	1	trivial
1932.2.u.a	✓	64	7.d	odd	6	1	inner
1932.2.u.a	✓	64	23.b	odd	2	1	inner
1932.2.u.a	✓	64	161.g	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1932, [\chi])\).