Space of modular forms of level 243 and weight 3

• Label: 243.3
• Level: 243
• Weight: 3
• Dimension: 3360
• Nonzero newspaces: 5
• Newform subspaces: 24
• Sturm bound: 13122
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 243 = 3^{5} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 24 \)
Sturm bound:			\(13122\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(243))\).

	Total	New	Old
Modular forms	4563	3552	1011
Cusp forms	4185	3360	825
Eisenstein series	378	192	186

Trace form

3360 * q - 36 * q^2 - 54 * q^3 - 60 * q^4 - 36 * q^5 - 54 * q^6 - 60 * q^7 - 36 * q^8 - 54 * q^9 - 84 * q^10 - 36 * q^11 - 54 * q^12 - 60 * q^13 - 36 * q^14 - 54 * q^15 - 36 * q^16 - 36 * q^17 - 54 * q^18 - 21 * q^19 + 180 * q^20 - 54 * q^21 + 12 * q^22 + 45 * q^23 - 54 * q^24 - 42 * q^25 - 27 * q^26 - 54 * q^27 - 183 * q^28 - 117 * q^29 - 54 * q^30 - 150 * q^31 - 360 * q^32 - 54 * q^33 - 180 * q^34 - 279 * q^35 - 54 * q^36 - 183 * q^37 - 144 * q^38 - 54 * q^39 - 6 * q^40 + 180 * q^41 - 54 * q^42 + 120 * q^43 + 612 * q^44 - 54 * q^45 + 294 * q^46 + 288 * q^47 - 54 * q^48 + 84 * q^49 + 315 * q^50 - 54 * q^51 - 90 * q^52 - 27 * q^53 - 54 * q^54 - 219 * q^55 - 450 * q^56 - 54 * q^57 - 330 * q^58 - 414 * q^59 - 54 * q^60 - 348 * q^61 - 927 * q^62 - 54 * q^63 - 1446 * q^64 - 2034 * q^65 - 1566 * q^66 - 1131 * q^67 - 4491 * q^68 - 1242 * q^69 - 1590 * q^70 - 1656 * q^71 - 2646 * q^72 - 840 * q^73 - 2196 * q^74 - 729 * q^75 - 912 * q^76 - 1116 * q^77 - 486 * q^78 - 186 * q^79 - 81 * q^80 + 54 * q^81 + 321 * q^82 + 504 * q^83 + 1458 * q^84 + 720 * q^85 + 2124 * q^86 + 1458 * q^87 + 1860 * q^88 + 2475 * q^89 + 2106 * q^90 + 1680 * q^91 + 7794 * q^92 + 1350 * q^93 + 2406 * q^94 + 3960 * q^95 + 2970 * q^96 + 1551 * q^97 + 4743 * q^98 + 972 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(243))\)

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
243.3.b	\(\chi_{243}(242, \cdot)\)	243.3.b.a	1	1
		243.3.b.b	1
		243.3.b.c	2
		243.3.b.d	2
		243.3.b.e	2
		243.3.b.f	2
		243.3.b.g	2
		243.3.b.h	12
243.3.d	\(\chi_{243}(80, \cdot)\)	243.3.d.a	2	2
		243.3.d.b	2
		243.3.d.c	2
		243.3.d.d	2
		243.3.d.e	2
		243.3.d.f	2
		243.3.d.g	4
		243.3.d.h	4
		243.3.d.i	4
		243.3.d.j	24
243.3.f	\(\chi_{243}(26, \cdot)\)	243.3.f.a	30	6
		243.3.f.b	30
		243.3.f.c	30
		243.3.f.d	30
243.3.h	\(\chi_{243}(8, \cdot)\)	243.3.h.a	306	18
243.3.j	\(\chi_{243}(2, \cdot)\)	243.3.j.a	2862	54

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(243))\) into lower level spaces

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