Space of modular forms of level 135 and weight 3

• Label: 135.3
• Level: 135
• Weight: 3
• Dimension: 890
• Nonzero newspaces: 9
• Newform subspaces: 18
• Sturm bound: 3888
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 18 \)
Sturm bound:			\(3888\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(135))\).

	Total	New	Old
Modular forms	1416	986	430
Cusp forms	1176	890	286
Eisenstein series	240	96	144

Trace form

890 * q - 10 * q^2 - 12 * q^3 - 2 * q^4 + 5 * q^5 - 12 * q^6 - 6 * q^7 + 18 * q^8 - 24 * q^9 + q^10 - 2 * q^11 + 6 * q^12 + 26 * q^13 + 30 * q^14 - 15 * q^15 - 62 * q^16 - 34 * q^17 - 150 * q^18 - 64 * q^19 - 267 * q^20 - 312 * q^21 - 82 * q^22 - 292 * q^23 - 312 * q^24 - 43 * q^25 + 64 * q^26 + 156 * q^27 + 156 * q^28 + 480 * q^29 + 219 * q^30 - 6 * q^31 + 302 * q^32 + 258 * q^33 - 346 * q^34 - 448 * q^35 + 96 * q^36 - 356 * q^37 - 870 * q^38 - 354 * q^39 - 567 * q^40 - 866 * q^41 - 1188 * q^42 - 178 * q^43 - 1314 * q^44 - 441 * q^45 - 186 * q^46 - 490 * q^47 - 450 * q^48 + 454 * q^49 + 1190 * q^50 + 216 * q^51 + 838 * q^52 + 1124 * q^53 + 804 * q^54 + 442 * q^55 + 2430 * q^56 + 828 * q^57 + 694 * q^58 + 1470 * q^59 + 1254 * q^60 + 470 * q^61 + 1876 * q^62 + 1146 * q^63 + 74 * q^64 + 311 * q^65 + 798 * q^66 - 684 * q^67 - 752 * q^68 - 222 * q^69 - 1131 * q^70 - 926 * q^71 - 2232 * q^72 - 1054 * q^73 - 2970 * q^74 - 1137 * q^75 - 2366 * q^76 - 2618 * q^77 - 2100 * q^78 - 1290 * q^79 - 3088 * q^80 - 888 * q^81 - 1004 * q^82 - 1570 * q^83 + 12 * q^84 - 317 * q^85 - 1394 * q^86 + 294 * q^87 + 1134 * q^88 - 180 * q^89 - 84 * q^90 + 150 * q^91 + 1658 * q^92 - 630 * q^93 + 2654 * q^94 + 957 * q^95 + 924 * q^96 + 1720 * q^97 + 2140 * q^98 + 150 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(135))\)

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
135.3.c	\(\chi_{135}(26, \cdot)\)	135.3.c.a	2	1
		135.3.c.b	4
		135.3.c.c	4
135.3.d	\(\chi_{135}(134, \cdot)\)	135.3.d.a	2	1
		135.3.d.b	2
		135.3.d.c	2
		135.3.d.d	2
		135.3.d.e	2
		135.3.d.f	2
		135.3.d.g	4
135.3.g	\(\chi_{135}(28, \cdot)\)	135.3.g.a	16	2
		135.3.g.b	16
135.3.h	\(\chi_{135}(44, \cdot)\)	135.3.h.a	20	2
135.3.i	\(\chi_{135}(71, \cdot)\)	135.3.i.a	16	2
135.3.l	\(\chi_{135}(37, \cdot)\)	135.3.l.a	40	4
135.3.n	\(\chi_{135}(14, \cdot)\)	135.3.n.a	204	6
135.3.o	\(\chi_{135}(11, \cdot)\)	135.3.o.a	144	6
135.3.r	\(\chi_{135}(7, \cdot)\)	135.3.r.a	408	12

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(135))\) into lower level spaces

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