Space of modular forms of level 108 and weight 6

• Label: 108.6
• Level: 108
• Weight: 6
• Dimension: 731
• Nonzero newspaces: 6
• Newform subspaces: 11
• Sturm bound: 3888
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(3888\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(108))\).

	Total	New	Old
Modular forms	1695	763	932
Cusp forms	1545	731	814
Eisenstein series	150	32	118

Trace form

731 * q - 3 * q^2 + 3 * q^4 - 72 * q^5 - 6 * q^6 - 2 * q^7 - 9 * q^8 + 318 * q^9 - 405 * q^10 - 1434 * q^11 + 1173 * q^12 + 568 * q^13 + 3027 * q^14 + 531 * q^15 - 2685 * q^16 - 5766 * q^17 - 5697 * q^18 - 209 * q^19 + 2475 * q^20 + 12882 * q^21 + 4803 * q^22 + 7707 * q^23 + 8988 * q^24 - 6736 * q^25 - 17415 * q^27 - 7206 * q^28 + 33375 * q^29 - 18135 * q^30 + 2896 * q^31 + 14457 * q^32 + 12342 * q^33 + 1431 * q^34 - 45375 * q^35 + 35664 * q^36 - 40325 * q^37 + 29745 * q^38 - 10545 * q^39 + 13419 * q^40 + 174162 * q^41 - 25506 * q^42 + 57448 * q^43 - 158049 * q^44 - 35781 * q^45 - 27651 * q^46 - 31932 * q^47 + 14469 * q^48 - 93090 * q^49 + 66756 * q^50 + 42831 * q^51 - 3465 * q^52 - 120990 * q^53 + 231414 * q^54 - 75942 * q^55 + 172449 * q^56 + 72048 * q^57 + 10743 * q^58 + 95925 * q^59 - 326058 * q^60 + 92380 * q^61 - 461448 * q^62 - 98115 * q^63 + 14637 * q^64 - 95976 * q^65 - 24771 * q^66 + 16903 * q^67 + 357870 * q^68 + 345801 * q^69 + 227715 * q^70 - 161556 * q^71 + 110388 * q^72 - 292772 * q^73 + 40803 * q^74 - 75273 * q^75 + 111135 * q^76 + 183600 * q^77 + 178248 * q^78 + 62164 * q^79 - 7926 * q^81 + 63030 * q^82 + 152226 * q^83 - 307308 * q^84 - 125652 * q^85 - 558483 * q^86 - 201483 * q^87 - 198645 * q^88 - 222162 * q^89 - 840048 * q^90 - 421192 * q^91 - 600627 * q^92 - 526815 * q^93 - 156753 * q^94 + 251274 * q^95 + 992022 * q^96 + 190771 * q^97 + 1307970 * q^98 + 13635 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(108))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
108.6.a	\(\chi_{108}(1, \cdot)\)	108.6.a.a	1	1
		108.6.a.b	2
		108.6.a.c	2
		108.6.a.d	2
108.6.b	\(\chi_{108}(107, \cdot)\)	108.6.b.a	4	1
		108.6.b.b	16
		108.6.b.c	20
108.6.e	\(\chi_{108}(37, \cdot)\)	108.6.e.a	10	2
108.6.h	\(\chi_{108}(35, \cdot)\)	108.6.h.a	56	2
108.6.i	\(\chi_{108}(13, \cdot)\)	108.6.i.a	90	6
108.6.l	\(\chi_{108}(11, \cdot)\)	108.6.l.a	528	6

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(108))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(108)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)