Space of modular forms of level 108 and weight 4

• Label: 108.4
• Level: 108
• Weight: 4
• Dimension: 432
• Nonzero newspaces: 6
• Newform subspaces: 11
• Sturm bound: 2592
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(2592\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(108))\).

	Total	New	Old
Modular forms	1047	464	583
Cusp forms	897	432	465
Eisenstein series	150	32	118

Trace form

432 * q - 3 * q^2 - 13 * q^4 - 6 * q^6 - 28 * q^7 - 9 * q^8 - 60 * q^9 + 43 * q^10 - 138 * q^11 - 123 * q^12 - 24 * q^13 + 147 * q^14 + 234 * q^15 + 131 * q^16 + 408 * q^17 + 351 * q^18 + 170 * q^19 + 459 * q^20 - 24 * q^21 + 195 * q^22 - 114 * q^23 - 300 * q^24 - 887 * q^25 + 27 * q^27 - 6 * q^28 - 312 * q^29 - 207 * q^30 + 92 * q^31 - 1383 * q^32 + 921 * q^33 - 905 * q^34 + 1110 * q^35 - 1056 * q^36 + 828 * q^37 - 1791 * q^38 + 66 * q^39 - 725 * q^40 + 264 * q^41 + 2574 * q^42 - 1492 * q^43 + 2655 * q^44 - 978 * q^45 + 1101 * q^46 - 2070 * q^47 - 435 * q^48 + 407 * q^49 - 852 * q^50 - 1368 * q^51 + 2167 * q^52 + 1140 * q^53 - 4458 * q^54 + 918 * q^55 + 81 * q^56 - 609 * q^57 + 2455 * q^58 - 1671 * q^59 + 966 * q^60 - 2040 * q^61 + 1872 * q^62 + 30 * q^63 - 163 * q^64 - 2412 * q^65 + 3093 * q^66 - 3502 * q^67 - 2634 * q^68 - 96 * q^69 - 6333 * q^70 - 240 * q^71 - 4524 * q^72 - 360 * q^73 - 11757 * q^74 + 732 * q^75 - 5121 * q^76 + 378 * q^77 - 2976 * q^78 + 3356 * q^79 + 3792 * q^81 + 2614 * q^82 + 5076 * q^83 + 6324 * q^84 + 5018 * q^85 + 16653 * q^86 + 4824 * q^87 + 10251 * q^88 + 9165 * q^89 - 1104 * q^90 + 2278 * q^91 + 5469 * q^92 + 8568 * q^93 + 6351 * q^94 + 534 * q^95 + 582 * q^96 - 504 * q^97 + 2898 * q^98 - 5076 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(108))\)

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
108.4.a	\(\chi_{108}(1, \cdot)\)	108.4.a.a	1	1
		108.4.a.b	1
		108.4.a.c	1
		108.4.a.d	1
108.4.b	\(\chi_{108}(107, \cdot)\)	108.4.b.a	12	1
		108.4.b.b	12
108.4.e	\(\chi_{108}(37, \cdot)\)	108.4.e.a	6	2
108.4.h	\(\chi_{108}(35, \cdot)\)	108.4.h.a	8	2
		108.4.h.b	24
108.4.i	\(\chi_{108}(13, \cdot)\)	108.4.i.a	54	6
108.4.l	\(\chi_{108}(11, \cdot)\)	108.4.l.a	312	6

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(108))\) into lower level spaces

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