Space of modular forms of level 135 and weight 2

• Label: 135.2
• Level: 135
• Weight: 2
• Dimension: 422
• Nonzero newspaces: 9
• Newform subspaces: 16
• Sturm bound: 2592
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 16 \)
Sturm bound:			\(2592\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(135))\).

	Total	New	Old
Modular forms	768	518	250
Cusp forms	529	422	107
Eisenstein series	239	96	143

Trace form

422 * q - 4 * q^2 - 12 * q^3 - 12 * q^4 - 13 * q^5 - 48 * q^6 - 14 * q^7 - 36 * q^8 - 24 * q^9 - 33 * q^10 - 46 * q^11 - 48 * q^12 - 34 * q^13 - 66 * q^14 - 33 * q^15 - 80 * q^16 - 46 * q^17 - 42 * q^18 - 16 * q^19 - 45 * q^20 - 24 * q^21 - 58 * q^22 - 12 * q^23 + 12 * q^24 - 37 * q^25 - 4 * q^26 - 6 * q^27 - 60 * q^28 - 32 * q^29 - 15 * q^30 - 70 * q^31 + 16 * q^32 - 12 * q^33 - 46 * q^34 + 8 * q^35 - 12 * q^36 - 36 * q^37 - 16 * q^38 - 30 * q^39 + 31 * q^40 + 10 * q^41 + 36 * q^42 + 14 * q^43 + 166 * q^44 + 45 * q^45 - 10 * q^46 + 98 * q^47 + 126 * q^48 + 152 * q^50 + 36 * q^51 + 30 * q^52 + 80 * q^53 + 156 * q^54 - 60 * q^55 + 66 * q^56 + 18 * q^57 - 70 * q^58 - 28 * q^59 + 48 * q^60 - 126 * q^61 - 84 * q^62 - 42 * q^63 - 84 * q^64 - 87 * q^65 - 30 * q^66 - 56 * q^67 - 62 * q^68 - 42 * q^69 - 45 * q^70 - 158 * q^71 + 36 * q^72 - 34 * q^73 - 14 * q^74 - 21 * q^75 + 28 * q^76 + 54 * q^77 + 96 * q^78 + 94 * q^79 + 150 * q^80 - 24 * q^81 + 120 * q^82 + 78 * q^83 + 192 * q^84 + 63 * q^85 + 170 * q^86 + 78 * q^87 + 168 * q^88 + 186 * q^89 + 186 * q^90 + 38 * q^91 + 402 * q^92 + 198 * q^93 + 146 * q^94 + 165 * q^95 + 168 * q^96 + 60 * q^97 + 370 * q^98 + 150 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)

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
135.2.a	\(\chi_{135}(1, \cdot)\)	135.2.a.a	1	1
		135.2.a.b	1
		135.2.a.c	2
		135.2.a.d	2
135.2.b	\(\chi_{135}(109, \cdot)\)	135.2.b.a	4	1
		135.2.b.b	4
135.2.e	\(\chi_{135}(46, \cdot)\)	135.2.e.a	2	2
		135.2.e.b	6
135.2.f	\(\chi_{135}(53, \cdot)\)	135.2.f.a	8	2
		135.2.f.b	8
135.2.j	\(\chi_{135}(19, \cdot)\)	135.2.j.a	8	2
135.2.k	\(\chi_{135}(16, \cdot)\)	135.2.k.a	30	6
		135.2.k.b	42
135.2.m	\(\chi_{135}(8, \cdot)\)	135.2.m.a	16	4
135.2.p	\(\chi_{135}(4, \cdot)\)	135.2.p.a	96	6
135.2.q	\(\chi_{135}(2, \cdot)\)	135.2.q.a	192	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(135))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(135)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 1}\)