Newform orbit 2052.3.bl.a

• Label: 2052.3.bl.a
• Level: $2052$
• Weight: $3$
• Character orbit: 2052.bl
• 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.bl (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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
145.1		0			0			0		−8.90430				0		−2.28143	−	3.95155i		0			0			0
145.2		0			0			0		−8.37687				0		−4.50755	−	7.80731i		0			0			0
145.3		0			0			0		−8.35221				0		0.352343	+	0.610277i		0			0			0
145.4		0			0			0		−7.87469				0		2.97107	+	5.14604i		0			0			0
145.5		0			0			0		−6.99525				0		0.133800	+	0.231748i		0			0			0
145.6		0			0			0		−6.81841				0		3.70019	+	6.40891i		0			0			0
145.7		0			0			0		−6.03262				0		−3.98752	−	6.90658i		0			0			0
145.8		0			0			0		−5.96221				0		6.83689	+	11.8418i		0			0			0
145.9		0			0			0		−5.52048				0		0.838417	+	1.45218i		0			0			0
145.10		0			0			0		−4.76547				0		3.51868	+	6.09454i		0			0			0
145.11		0			0			0		−4.14557				0		−5.99339	−	10.3809i		0			0			0
145.12		0			0			0		−4.10591				0		−6.48935	−	11.2399i		0			0			0
145.13		0			0			0		−3.96127				0		2.79341	+	4.83834i		0			0			0
145.14		0			0			0		−3.77174				0		−0.501515	−	0.868649i		0			0			0
145.15		0			0			0		−3.57346				0		2.11933	+	3.67079i		0			0			0
145.16		0			0			0		−3.05736				0		−5.58622	−	9.67561i		0			0			0
145.17		0			0			0		−1.84061				0		3.31490	+	5.74157i		0			0			0
145.18		0			0			0		−0.638534				0		−1.11619	−	1.93329i		0			0			0
145.19		0			0			0		−0.387901				0		5.33508	+	9.24062i		0			0			0
145.20		0			0			0		−0.356865				0		−3.52002	−	6.09686i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
171.s	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.bl.a		80
3.b	odd	2	1		684.3.bl.a	yes	80
9.c	even	3	1		2052.3.s.a		80
9.d	odd	6	1		684.3.s.a	✓	80
19.d	odd	6	1		2052.3.s.a		80
57.f	even	6	1		684.3.s.a	✓	80
171.k	even	6	1		684.3.bl.a	yes	80
171.s	odd	6	1	inner	2052.3.bl.a		80

    

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

Hecke kernels

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