Newform orbit 2052.3.m.a

• Label: 2052.3.m.a
• Level: $2052$
• Weight: $3$
• Character orbit: 2052.m
• 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.m (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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
881.1		0			0			0			−	9.28650i		0		−2.28067	−	3.95023i		0			0			0
881.2		0			0			0			−	8.16148i		0		−1.62444	−	2.81362i		0			0			0
881.3		0			0			0			−	7.26979i		0		3.75776	+	6.50863i		0			0			0
881.4		0			0			0			−	7.03696i		0		2.95479	+	5.11784i		0			0			0
881.5		0			0			0			−	6.78017i		0		−0.841737	−	1.45793i		0			0			0
881.6		0			0			0			−	6.34957i		0		−3.73312	−	6.46596i		0			0			0
881.7		0			0			0			−	6.32167i		0		2.00114	+	3.46607i		0			0			0
881.8		0			0			0			−	6.24143i		0		4.14502	+	7.17938i		0			0			0
881.9		0			0			0			−	6.14879i		0		−6.67945	−	11.5692i		0			0			0
881.10		0			0			0			−	5.73236i		0		5.68826	+	9.85235i		0			0			0
881.11		0			0			0			−	5.68625i		0		−1.27053	−	2.20061i		0			0			0
881.12		0			0			0			−	4.55087i		0		5.85150	+	10.1351i		0			0			0
881.13		0			0			0			−	3.96092i		0		−6.03683	−	10.4561i		0			0			0
881.14		0			0			0			−	2.92593i		0		−2.71227	−	4.69779i		0			0			0
881.15		0			0			0			−	2.23654i		0		1.30590	+	2.26189i		0			0			0
881.16		0			0			0			−	1.84834i		0		2.46982	+	4.27785i		0			0			0
881.17		0			0			0			−	1.38038i		0		−1.29258	−	2.23881i		0			0			0
881.18		0			0			0			−	0.944063i		0		−5.01764	−	8.69081i		0			0			0
881.19		0			0			0			−	0.497329i		0		5.73504	+	9.93338i		0			0			0
881.20		0			0			0			−	0.434480i		0		−4.09970	−	7.10089i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
171.n	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.m.a		80
3.b	odd	2	1		684.3.m.a	✓	80
9.c	even	3	1		684.3.be.a	yes	80
9.d	odd	6	1		2052.3.be.a		80
19.c	even	3	1		2052.3.be.a		80
57.h	odd	6	1		684.3.be.a	yes	80
171.g	even	3	1		684.3.m.a	✓	80
171.n	odd	6	1	inner	2052.3.m.a		80

    

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

Hecke kernels

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