Newform orbit 2052.3.be.a

• Label: 2052.3.be.a
• Level: $2052$
• Weight: $3$
• Character orbit: 2052.be
• Analytic conductor: $55.913$
• Analytic rank: $0$
• Dimension: $80$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2052 = 2^{2} \cdot 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2052.be (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(55.9129502467\)
Analytic rank:	\(0\)
Dimension:	\(80\)
Relative dimension:	\(40\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 684)
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.

\(\operatorname{Tr}(f)(q) = \) \( 80 q + q^{7}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
125.1		0			0			0		−8.04234	+	4.64325i		0		−2.28067	−	3.95023i		0			0			0
125.2		0			0			0		−7.06805	+	4.08074i		0		−1.62444	−	2.81362i		0			0			0
125.3		0			0			0		−6.29582	+	3.63489i		0		3.75776	+	6.50863i		0			0			0
125.4		0			0			0		−6.09418	+	3.51848i		0		2.95479	+	5.11784i		0			0			0
125.5		0			0			0		−5.87180	+	3.39009i		0		−0.841737	−	1.45793i		0			0			0
125.6		0			0			0		−5.49889	+	3.17478i		0		−3.73312	−	6.46596i		0			0			0
125.7		0			0			0		−5.47473	+	3.16084i		0		2.00114	+	3.46607i		0			0			0
125.8		0			0			0		−5.40523	+	3.12071i		0		4.14502	+	7.17938i		0			0			0
125.9		0			0			0		−5.32501	+	3.07440i		0		−6.67945	−	11.5692i		0			0			0
125.10		0			0			0		−4.96437	+	2.86618i		0		5.68826	+	9.85235i		0			0			0
125.11		0			0			0		−4.92443	+	2.84312i		0		−1.27053	−	2.20061i		0			0			0
125.12		0			0			0		−3.94117	+	2.27544i		0		5.85150	+	10.1351i		0			0			0
125.13		0			0			0		−3.43026	+	1.98046i		0		−6.03683	−	10.4561i		0			0			0
125.14		0			0			0		−2.53393	+	1.46297i		0		−2.71227	−	4.69779i		0			0			0
125.15		0			0			0		−1.93690	+	1.11827i		0		1.30590	+	2.26189i		0			0			0
125.16		0			0			0		−1.60071	+	0.924171i		0		2.46982	+	4.27785i		0			0			0
125.17		0			0			0		−1.19545	+	0.690191i		0		−1.29258	−	2.23881i		0			0			0
125.18		0			0			0		−0.817582	+	0.472031i		0		−5.01764	−	8.69081i		0			0			0
125.19		0			0			0		−0.430700	+	0.248665i		0		5.73504	+	9.93338i		0			0			0
125.20		0			0			0		−0.376271	+	0.217240i		0		−4.09970	−	7.10089i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
171.j	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2052.3.be.a		80
3.b	odd	2	1		684.3.be.a	yes	80
9.c	even	3	1		684.3.m.a	✓	80
9.d	odd	6	1		2052.3.m.a		80
19.c	even	3	1		2052.3.m.a		80
57.h	odd	6	1		684.3.m.a	✓	80
171.h	even	3	1		684.3.be.a	yes	80
171.j	odd	6	1	inner	2052.3.be.a		80

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
684.3.m.a	✓	80	9.c	even	3	1
684.3.m.a	✓	80	57.h	odd	6	1
684.3.be.a	yes	80	3.b	odd	2	1
684.3.be.a	yes	80	171.h	even	3	1
2052.3.m.a		80	9.d	odd	6	1
2052.3.m.a		80	19.c	even	3	1
2052.3.be.a		80	1.a	even	1	1	trivial
2052.3.be.a		80	171.j	odd	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(2052, [\chi])\).