Space of modular forms of level 2052, weight 3, and Character 2052.be

• Label: 2052.3.be
• Level: $2052$
• Weight: $3$
• Character orbit: 2052.be
• Rep. character: $\chi_{2052}(125,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $1080$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2052 = 2^{2} \cdot 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2052.be (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 171 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(1080\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2052, [\chi])\).

	Total	New	Old
Modular forms	1476	80	1396
Cusp forms	1404	80	1324
Eisenstein series	72	0	72

Trace form

\( 80 q + q^{7} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2052, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2052.3.be.a	$2052$	$3$	2052.be	171.j	$6$	$80$	$40$	$55.913$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(2052, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2052, [\chi]) \cong \)