Space of modular forms of level 108, weight 2, and Character 108.h

• Label: 108.2.h
• Level: $108$
• Weight: $2$
• Character orbit: 108.h
• Rep. character: $\chi_{108}(35,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(108, [\chi])\).

	Total	New	Old
Modular forms	48	16	32
Cusp forms	24	8	16
Eisenstein series	24	8	16

Trace form

\( 8 q + 3 q^{2} - q^{4} + 6 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(108, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
108.2.h.a	$108$	$2$	108.h	36.h	$6$	$8$	$4$	$0.862$	8.0.170772624.1	None		$4$	$0$	\(3\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{5}-\beta _{7})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)