Space of modular forms of level 108, weight 4, and Character 108.e

• Label: 108.4.e
• Level: $108$
• Weight: $4$
• Character orbit: 108.e
• Rep. character: $\chi_{108}(37,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(108, [\chi])\).

	Total	New	Old
Modular forms	126	6	120
Cusp forms	90	6	84
Eisenstein series	36	0	36

Trace form

\( 6 q - 6 q^{5} - 6 q^{7} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(108, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
108.4.e.a	$108$	$4$	108.e	9.c	$3$	$6$	$3$	$6.372$	6.0.6831243.2	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(-6\)	$2^{2}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\beta _{1}+\beta _{5})q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)