Space of modular forms of level 108 and weight 9

• Label: 108.9
• Level: 108
• Weight: 9
• Dimension: 1179
• Nonzero newspaces: 6
• Sturm bound: 5832
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(5832\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(108))\).

	Total	New	Old
Modular forms	2667	1211	1456
Cusp forms	2517	1179	1338
Eisenstein series	150	32	118

Trace form

1179 * q - 5 * q^2 + 231 * q^4 - 892 * q^5 - 6 * q^6 + 3384 * q^7 + 9955 * q^8 - 12966 * q^9 - 20481 * q^10 + 10980 * q^11 - 12921 * q^12 + 48246 * q^13 + 35847 * q^14 - 176535 * q^15 - 340605 * q^16 - 27550 * q^17 + 424089 * q^18 + 73797 * q^19 + 288167 * q^20 + 650190 * q^21 - 1018437 * q^22 - 1690209 * q^23 + 101166 * q^24 + 3049083 * q^25 + 5026418 * q^26 - 271026 * q^27 - 1245414 * q^28 + 5379035 * q^29 - 2434689 * q^30 - 138270 * q^31 + 9139465 * q^32 - 12400827 * q^33 + 1869363 * q^34 + 6225417 * q^35 - 5216376 * q^36 + 3894885 * q^37 - 14676759 * q^38 + 1460577 * q^39 + 5389011 * q^40 - 7632322 * q^41 + 43288434 * q^42 - 3522 * q^43 - 10294101 * q^44 - 23322309 * q^45 - 14850279 * q^46 - 14266206 * q^47 + 16303245 * q^48 - 18167421 * q^49 + 75648708 * q^50 + 55996821 * q^51 + 550263 * q^52 - 7237456 * q^53 - 50485602 * q^54 - 15252804 * q^55 - 146503899 * q^56 - 59399529 * q^57 + 41505363 * q^58 + 93924216 * q^59 + 86071458 * q^60 - 37273386 * q^61 + 9608670 * q^62 + 47793945 * q^63 + 25926921 * q^64 - 114252710 * q^65 - 103641915 * q^66 - 89386905 * q^67 + 12209876 * q^68 + 183254493 * q^69 - 29216349 * q^70 + 125718804 * q^71 - 10214844 * q^72 - 12700842 * q^73 - 248754397 * q^74 - 228256323 * q^75 - 173978457 * q^76 - 147301920 * q^77 + 185351214 * q^78 + 49908234 * q^79 + 392808878 * q^80 + 145725654 * q^81 + 50668626 * q^82 + 79364502 * q^83 - 264278694 * q^84 + 120109512 * q^85 - 657058275 * q^86 - 227735505 * q^87 - 93881445 * q^88 - 500713867 * q^89 - 45364614 * q^90 + 157223214 * q^91 - 86219847 * q^92 + 500172417 * q^93 - 51613761 * q^94 + 645227820 * q^95 + 924779850 * q^96 + 644328447 * q^97 + 370270900 * q^98 - 549573633 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(108))\)

We only show spaces with odd 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
108.9.c	\(\chi_{108}(53, \cdot)\)	108.9.c.a	1	1
		108.9.c.b	2
		108.9.c.c	2
		108.9.c.d	6
108.9.d	\(\chi_{108}(55, \cdot)\)	108.9.d.a	32	1
		108.9.d.b	32
108.9.f	\(\chi_{108}(19, \cdot)\)	108.9.f.a	92	2
108.9.g	\(\chi_{108}(17, \cdot)\)	108.9.g.a	16	2
108.9.j	\(\chi_{108}(7, \cdot)\)	n/a	852	6
108.9.k	\(\chi_{108}(5, \cdot)\)	n/a	144	6

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(108))\) into lower level spaces

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