Space of modular forms of level 135 and weight 4

• Label: 135.4
• Level: 135
• Weight: 4
• Dimension: 1360
• Nonzero newspaces: 9
• Newform subspaces: 22
• Sturm bound: 5184
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 22 \)
Sturm bound:			\(5184\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(135))\).

	Total	New	Old
Modular forms	2064	1456	608
Cusp forms	1824	1360	464
Eisenstein series	240	96	144

Trace form

1360 * q - 10 * q^2 - 12 * q^3 - 50 * q^4 - 37 * q^5 - 12 * q^6 + 54 * q^7 + 234 * q^8 + 84 * q^9 - 31 * q^10 - 262 * q^11 - 318 * q^12 - 138 * q^13 - 18 * q^14 + 12 * q^15 + 546 * q^16 + 890 * q^17 + 1254 * q^18 + 114 * q^19 + 81 * q^20 + 228 * q^21 - 850 * q^22 - 1326 * q^23 - 2364 * q^24 - 59 * q^25 - 4372 * q^26 - 2274 * q^27 - 116 * q^28 - 182 * q^29 - 483 * q^30 + 1250 * q^31 + 4294 * q^32 + 2310 * q^33 + 2390 * q^34 + 3983 * q^35 + 6144 * q^36 + 1422 * q^37 + 2678 * q^38 + 672 * q^39 - 3007 * q^40 - 218 * q^41 + 2484 * q^42 - 3066 * q^43 - 5810 * q^44 - 2304 * q^45 - 4802 * q^46 - 8134 * q^47 - 8442 * q^48 - 2854 * q^49 - 6676 * q^50 - 5454 * q^51 + 1326 * q^52 - 1792 * q^53 - 7620 * q^54 + 2552 * q^55 + 702 * q^56 - 2844 * q^57 + 3894 * q^58 - 604 * q^59 + 1254 * q^60 - 742 * q^61 + 5856 * q^62 + 5196 * q^63 + 5682 * q^64 + 7881 * q^65 + 22182 * q^66 + 6738 * q^67 + 23044 * q^68 + 12252 * q^69 + 4845 * q^70 + 11794 * q^71 + 6192 * q^72 + 2598 * q^73 + 11134 * q^74 + 7584 * q^75 - 46 * q^76 + 2394 * q^77 - 5448 * q^78 - 4578 * q^79 - 7686 * q^80 - 8556 * q^81 - 8092 * q^82 - 17922 * q^83 - 28824 * q^84 - 11947 * q^85 - 39754 * q^86 - 15744 * q^87 - 27858 * q^88 - 17976 * q^89 - 7806 * q^90 - 12294 * q^91 + 762 * q^92 + 12492 * q^93 + 5726 * q^94 - 1623 * q^95 + 17988 * q^96 + 7854 * q^97 + 2188 * q^98 + 2580 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(135))\)

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
135.4.a	\(\chi_{135}(1, \cdot)\)	135.4.a.a	1	1
		135.4.a.b	1
		135.4.a.c	1
		135.4.a.d	1
		135.4.a.e	3
		135.4.a.f	3
		135.4.a.g	3
		135.4.a.h	3
135.4.b	\(\chi_{135}(109, \cdot)\)	135.4.b.a	4	1
		135.4.b.b	8
		135.4.b.c	12
135.4.e	\(\chi_{135}(46, \cdot)\)	135.4.e.a	4	2
		135.4.e.b	6
		135.4.e.c	14
135.4.f	\(\chi_{135}(53, \cdot)\)	135.4.f.a	24	2
		135.4.f.b	24
135.4.j	\(\chi_{135}(19, \cdot)\)	135.4.j.a	32	2
135.4.k	\(\chi_{135}(16, \cdot)\)	135.4.k.a	102	6
		135.4.k.b	114
135.4.m	\(\chi_{135}(8, \cdot)\)	135.4.m.a	64	4
135.4.p	\(\chi_{135}(4, \cdot)\)	135.4.p.a	312	6
135.4.q	\(\chi_{135}(2, \cdot)\)	135.4.q.a	624	12

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(135))\) into lower level spaces

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