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

• Label: 108.6.e
• Level: $108$
• Weight: $6$
• Character orbit: 108.e
• Rep. character: $\chi_{108}(37,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	198	10	188
Cusp forms	162	10	152
Eisenstein series	36	0	36

Trace form

10 * q + 21 * q^5 + 29 * q^7 - 177 * q^11 - 181 * q^13 - 2280 * q^17 - 832 * q^19 - 399 * q^23 - 4778 * q^25 + 6033 * q^29 + 2759 * q^31 - 37146 * q^35 - 15172 * q^37 + 18435 * q^41 + 1469 * q^43 + 25155 * q^47 - 4056 * q^49 - 116844 * q^53 + 14778 * q^55 + 90537 * q^59 + 1403 * q^61 + 148407 * q^65 + 13907 * q^67 - 229368 * q^71 + 15200 * q^73 + 211983 * q^77 + 29993 * q^79 + 228951 * q^83 - 49662 * q^85 - 598332 * q^89 + 124930 * q^91 + 394764 * q^95 + 40541 * q^97

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
108.6.e.a	$108$	$6$	108.e	9.c	$3$	$10$	$5$	$17.321$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None			✓	✓	36.6.e.a	$2$	$0$	\(0\)	\(0\)	\(21\)	\(29\)	$2^{8}\cdot 3^{16}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(4-4\beta _{1}+\beta _{7})q^{5}+(6\beta _{1}+\beta _{2}+\beta _{7}+\cdots)q^{7}+\cdots\)

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

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