Space of modular forms of level 108, weight 6, and trivial character

• Label: 108.6.a
• Level: $108$
• Weight: $6$
• Character orbit: 108.a
• Rep. character: $\chi_{108}(1,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $4$
• Sturm bound: $108$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(108\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(108))\).

	Total	New	Old
Modular forms	99	7	92
Cusp forms	81	7	74
Eisenstein series	18	0	18

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	Fricke	Dim
\(-\)	\(+\)	$-$	\(4\)
\(-\)	\(-\)	$+$	\(3\)
Plus space		\(+\)	\(3\)
Minus space		\(-\)	\(4\)

Trace form

\( 7 q - 31 q^{7} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(108))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3
108.6.a.a	$108$	$6$	108.a	1.a	$1$	$1$	$1$	$17.321$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-25\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-5^{2}q^{7}-427q^{13}-1711q^{19}-5^{5}q^{25}+\cdots\)
108.6.a.b	$108$	$6$	108.a	1.a	$1$	$2$	$2$	$17.321$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-32\)		$-$	$-$	$+$	$2\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-\beta q^{5}+(-2^{4}+3\beta )q^{7}+(-3^{5}+8\beta )q^{11}+\cdots\)
108.6.a.c	$108$	$6$	108.a	1.a	$1$	$2$	$2$	$17.321$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-32\)		$-$	$+$	$-$	$2\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-\beta q^{5}+(-2^{4}-3\beta )q^{7}+(3^{5}+8\beta )q^{11}+\cdots\)
108.6.a.d	$108$	$6$	108.a	1.a	$1$	$2$	$2$	$17.321$	\(\Q(\sqrt{6}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(58\)		$-$	$+$	$-$	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+29q^{7}+\beta q^{11}+329q^{13}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(108))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(108)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 2}\)