Space of modular forms of level 108 and weight 2

• Label: 108.2
• Level: 108
• Weight: 2
• Dimension: 133
• Nonzero newspaces: 6
• Newform subspaces: 7
• Sturm bound: 1296
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(1296\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(108))\).

	Total	New	Old
Modular forms	399	165	234
Cusp forms	250	133	117
Eisenstein series	149	32	117

Trace form

133 * q - 3 * q^2 - 5 * q^4 - 6 * q^6 + 6 * q^7 - 9 * q^8 - 6 * q^9 - 13 * q^10 + 6 * q^11 - 15 * q^12 - 16 * q^13 - 33 * q^14 - 9 * q^15 - 29 * q^16 - 42 * q^17 - 27 * q^18 - 9 * q^19 - 45 * q^20 - 42 * q^21 - 21 * q^22 - 33 * q^23 - 12 * q^24 - 30 * q^25 - 27 * q^27 - 6 * q^28 - 51 * q^29 + 9 * q^30 + 57 * q^32 - 60 * q^33 + 23 * q^34 - 15 * q^35 + 24 * q^36 - 31 * q^37 + 45 * q^38 + 3 * q^39 + 11 * q^40 - 42 * q^41 + 54 * q^42 + 63 * q^44 + 21 * q^45 + 9 * q^46 + 36 * q^47 + 69 * q^48 - 32 * q^49 + 66 * q^50 + 63 * q^51 - 25 * q^52 + 78 * q^53 + 78 * q^54 + 18 * q^55 + 81 * q^56 + 30 * q^57 - 25 * q^58 + 57 * q^59 + 102 * q^60 - 4 * q^61 + 90 * q^62 + 57 * q^63 + 13 * q^64 + 72 * q^65 + 87 * q^66 - 9 * q^67 + 66 * q^68 + 3 * q^69 + 27 * q^70 + 12 * q^71 + 12 * q^72 + 20 * q^73 + 51 * q^74 - 33 * q^75 + 15 * q^76 - 36 * q^77 - 24 * q^78 - 60 * q^79 - 42 * q^81 - 58 * q^82 - 54 * q^83 - 12 * q^84 - 80 * q^85 - 51 * q^86 - 63 * q^87 - 21 * q^88 - 60 * q^89 - 78 * q^90 - 24 * q^91 - 147 * q^92 + 27 * q^93 - 33 * q^94 - 6 * q^95 - 138 * q^96 - 67 * q^97 - 180 * q^98 + 27 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)

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
108.2.a	\(\chi_{108}(1, \cdot)\)	108.2.a.a	1	1
108.2.b	\(\chi_{108}(107, \cdot)\)	108.2.b.a	4	1
		108.2.b.b	4
108.2.e	\(\chi_{108}(37, \cdot)\)	108.2.e.a	2	2
108.2.h	\(\chi_{108}(35, \cdot)\)	108.2.h.a	8	2
108.2.i	\(\chi_{108}(13, \cdot)\)	108.2.i.a	18	6
108.2.l	\(\chi_{108}(11, \cdot)\)	108.2.l.a	96	6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(108))\) into lower level spaces

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