Space of modular forms of level 108, weight 3, and Character 108.g

• Label: 108.3.g
• Level: $108$
• Weight: $3$
• Character orbit: 108.g
• Rep. character: $\chi_{108}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $54$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(54\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(108, [\chi])\).

	Total	New	Old
Modular forms	90	4	86
Cusp forms	54	4	50
Eisenstein series	36	0	36

Trace form

4 * q - 9 * q^5 - q^7 + 36 * q^11 + 5 * q^13 + 2 * q^19 - 99 * q^23 + 13 * q^25 + 63 * q^29 - 7 * q^31 - 64 * q^37 + 18 * q^41 - 46 * q^43 + 81 * q^47 - 51 * q^49 + 90 * q^55 - 126 * q^59 + 41 * q^61 - 171 * q^65 + 116 * q^67 + 86 * q^73 + 279 * q^77 + 83 * q^79 + 81 * q^83 + 18 * q^85 - 302 * q^91 + 144 * q^95 - 196 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
108.3.g.a	$108$	$3$	108.g	9.d	$6$	$4$	$2$	$2.943$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None			✓	✓	36.3.g.a	$2$	$0$	\(0\)	\(0\)	\(-9\)	\(-1\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\beta _{2}-\beta _{3})q^{5}+(-1+\beta _{1}-2\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

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