Space of modular forms of level 108 and weight 3

• Label: 108.3
• Level: 108
• Weight: 3
• Dimension: 283
• Nonzero newspaces: 6
• Newform subspaces: 12
• Sturm bound: 1944
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(1944\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(108))\).

	Total	New	Old
Modular forms	723	315	408
Cusp forms	573	283	290
Eisenstein series	150	32	118

Trace form

283 * q - 5 * q^2 - 9 * q^4 - 28 * q^5 - 6 * q^6 - 4 * q^7 + 19 * q^8 - 6 * q^9 + 15 * q^10 + 72 * q^11 + 39 * q^12 + 50 * q^13 + 63 * q^14 + 45 * q^15 + 3 * q^16 + 26 * q^17 - 27 * q^18 - 19 * q^19 - 121 * q^20 + 30 * q^21 - 117 * q^22 - 117 * q^23 - 138 * q^24 - 35 * q^25 - 334 * q^26 - 198 * q^28 + 131 * q^29 - 153 * q^30 + 62 * q^31 - 215 * q^32 - 105 * q^33 - 45 * q^34 - 243 * q^35 + 24 * q^36 - 55 * q^37 + 225 * q^38 - 123 * q^39 + 243 * q^40 - 430 * q^41 - 126 * q^42 - 22 * q^43 + 171 * q^44 - 465 * q^45 + 273 * q^46 - 162 * q^47 - 219 * q^48 - 111 * q^49 + 72 * q^50 - 99 * q^51 + 87 * q^52 - 160 * q^53 + 78 * q^54 - 72 * q^55 - 171 * q^56 + 93 * q^57 - 429 * q^58 + 126 * q^59 + 210 * q^60 - 214 * q^61 - 270 * q^62 + 381 * q^63 - 327 * q^64 + 274 * q^65 + 393 * q^66 + 239 * q^67 + 44 * q^68 + 525 * q^69 - 141 * q^70 + 324 * q^71 + 228 * q^72 + 290 * q^73 + 851 * q^74 + 597 * q^75 + 615 * q^76 + 1152 * q^77 + 750 * q^78 + 350 * q^79 + 1646 * q^80 + 174 * q^81 + 786 * q^82 + 54 * q^83 + 762 * q^84 + 1053 * q^86 - 441 * q^87 + 219 * q^88 - 289 * q^89 + 894 * q^90 - 146 * q^91 + 297 * q^92 - 1719 * q^93 - 609 * q^94 - 900 * q^95 + 474 * q^96 - 325 * q^97 - 512 * q^98 - 945 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(108))\)

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
108.3.c	\(\chi_{108}(53, \cdot)\)	108.3.c.a	1	1
		108.3.c.b	2
108.3.d	\(\chi_{108}(55, \cdot)\)	108.3.d.a	2	1
		108.3.d.b	2
		108.3.d.c	4
		108.3.d.d	8
108.3.f	\(\chi_{108}(19, \cdot)\)	108.3.f.a	2	2
		108.3.f.b	2
		108.3.f.c	16
108.3.g	\(\chi_{108}(17, \cdot)\)	108.3.g.a	4	2
108.3.j	\(\chi_{108}(7, \cdot)\)	108.3.j.a	204	6
108.3.k	\(\chi_{108}(5, \cdot)\)	108.3.k.a	36	6

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(108))\) into lower level spaces

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