Space of modular forms of level 108, weight 6, and Character 108.b

• Label: 108.6.b
• Level: $108$
• Weight: $6$
• Character orbit: 108.b
• Rep. character: $\chi_{108}(107,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $3$
• Sturm bound: $108$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(108\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(108, [\chi])\).

	Total	New	Old
Modular forms	96	40	56
Cusp forms	84	40	44
Eisenstein series	12	0	12

Trace form

\( 40 q + 10 q^{4} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(108, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
108.6.b.a	$108$	$6$	108.b	12.b	$2$	$4$	$4$	$17.321$	\(\Q(\sqrt{3}, \sqrt{-29})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2})q^{2}+(-26-2\beta _{3})q^{4}+\cdots\)
108.6.b.b	$108$	$6$	108.b	12.b	$2$	$16$	$16$	$17.321$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{30}\cdot 3^{32}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(6-\beta _{4})q^{4}+(-3\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
108.6.b.c	$108$	$6$	108.b	12.b	$2$	$20$	$20$	$17.321$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{50}\cdot 3^{40}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+(1+\beta _{2})q^{4}+\beta _{15}q^{5}-\beta _{5}q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(108, [\chi]) \cong \)