Space of modular forms of level 729 and weight 2

• Label: 729.2
• Level: 729
• Weight: 2
• Dimension: 15228
• Nonzero newspaces: 6
• Newform subspaces: 37
• Sturm bound: 78732
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 729 = 3^{6} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 37 \)
Sturm bound:			\(78732\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(729))\).

	Total	New	Old
Modular forms	20331	15876	4455
Cusp forms	19036	15228	3808
Eisenstein series	1295	648	647

Trace form

15228 * q - 108 * q^2 - 162 * q^3 - 180 * q^4 - 108 * q^5 - 162 * q^6 - 180 * q^7 - 108 * q^8 - 162 * q^9 - 252 * q^10 - 108 * q^11 - 162 * q^12 - 180 * q^13 - 108 * q^14 - 162 * q^15 - 180 * q^16 - 108 * q^17 - 162 * q^18 - 252 * q^19 - 108 * q^20 - 162 * q^21 - 180 * q^22 - 108 * q^23 - 162 * q^24 - 180 * q^25 - 108 * q^26 - 162 * q^27 - 324 * q^28 - 108 * q^29 - 162 * q^30 - 180 * q^31 - 108 * q^32 - 162 * q^33 - 180 * q^34 - 108 * q^35 - 162 * q^36 - 252 * q^37 - 108 * q^38 - 162 * q^39 - 180 * q^40 - 108 * q^41 - 162 * q^42 - 180 * q^43 - 108 * q^44 - 162 * q^45 - 252 * q^46 - 108 * q^47 - 162 * q^48 - 180 * q^49 - 108 * q^50 - 162 * q^51 - 216 * q^52 - 108 * q^53 - 162 * q^54 - 324 * q^55 - 108 * q^56 - 162 * q^57 - 180 * q^58 - 108 * q^59 - 162 * q^60 - 180 * q^61 - 108 * q^62 - 162 * q^63 - 324 * q^64 - 162 * q^65 - 162 * q^66 - 234 * q^67 - 297 * q^68 - 162 * q^69 - 288 * q^70 - 216 * q^71 - 162 * q^72 - 333 * q^73 - 324 * q^74 - 162 * q^75 - 342 * q^76 - 324 * q^77 - 162 * q^78 - 288 * q^79 - 513 * q^80 - 162 * q^81 - 567 * q^82 - 216 * q^83 - 162 * q^84 - 288 * q^85 - 324 * q^86 - 162 * q^87 - 342 * q^88 - 243 * q^89 - 162 * q^90 - 333 * q^91 - 432 * q^92 - 162 * q^93 - 288 * q^94 - 216 * q^95 - 162 * q^96 - 234 * q^97 - 216 * q^98 - 162 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(729))\)

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
729.2.a	\(\chi_{729}(1, \cdot)\)	729.2.a.a	6	1
		729.2.a.b	6
		729.2.a.c	6
		729.2.a.d	6
		729.2.a.e	6
729.2.c	\(\chi_{729}(244, \cdot)\)	729.2.c.a	12	2
		729.2.c.b	12
		729.2.c.c	12
		729.2.c.d	12
		729.2.c.e	12
729.2.e	\(\chi_{729}(82, \cdot)\)	729.2.e.a	6	6
		729.2.e.b	6
		729.2.e.c	6
		729.2.e.d	6
		729.2.e.e	6
		729.2.e.f	6
		729.2.e.g	6
		729.2.e.h	6
		729.2.e.i	6
		729.2.e.j	12
		729.2.e.k	12
		729.2.e.l	12
		729.2.e.m	12
		729.2.e.n	12
		729.2.e.o	12
		729.2.e.p	12
		729.2.e.q	12
		729.2.e.r	12
		729.2.e.s	12
		729.2.e.t	12
		729.2.e.u	12
729.2.g	\(\chi_{729}(28, \cdot)\)	729.2.g.a	144	18
		729.2.g.b	144
		729.2.g.c	144
		729.2.g.d	144
729.2.i	\(\chi_{729}(10, \cdot)\)	729.2.i.a	1404	54
729.2.k	\(\chi_{729}(4, \cdot)\)	729.2.k.a	12960	162

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(729))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(729)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(729))\)\(^{\oplus 1}\)