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

• Label: 108.4.b
• Level: $108$
• Weight: $4$
• Character orbit: 108.b
• Rep. character: $\chi_{108}(107,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(72\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	60	24	36
Cusp forms	48	24	24
Eisenstein series	12	0	12

Trace form

\( 24 q - 6 q^{4} + O(q^{10}) \)

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.b.a	$108$	$4$	108.b	12.b	$2$	$12$	$12$	$6.372$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+(-1-\beta _{4})q^{4}-\beta _{9}q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
108.4.b.b	$108$	$4$	108.b	12.b	$2$	$12$	$12$	$6.372$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{6}q^{4}+\beta _{5}q^{5}-\beta _{4}q^{7}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(108, [\chi]) \cong \)