Space of modular forms of level 288 and weight 3

• Label: 288.3
• Level: 288
• Weight: 3
• Dimension: 2007
• Nonzero newspaces: 12
• Newform subspaces: 27
• Sturm bound: 13824
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 27 \)
Sturm bound:			\(13824\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(288))\).

	Total	New	Old
Modular forms	4864	2097	2767
Cusp forms	4352	2007	2345
Eisenstein series	512	90	422

Trace form

2007 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 8 * q^5 - 16 * q^6 - 10 * q^7 - 12 * q^8 - 24 * q^9 - 76 * q^10 - 28 * q^11 - 16 * q^12 - 40 * q^13 - 28 * q^14 - 30 * q^15 + 8 * q^16 - 62 * q^17 - 16 * q^18 - 58 * q^19 + 68 * q^20 - 48 * q^21 + 136 * q^22 - 70 * q^23 - 16 * q^24 + 31 * q^25 + 88 * q^26 + 36 * q^27 + 24 * q^28 + 152 * q^29 + 16 * q^30 + 122 * q^31 - 32 * q^32 + 76 * q^33 - 56 * q^34 + 288 * q^35 + 248 * q^36 + 224 * q^37 + 604 * q^38 + 102 * q^39 + 480 * q^40 + 294 * q^41 + 384 * q^42 + 200 * q^43 + 332 * q^44 + 80 * q^45 + 60 * q^46 + 6 * q^47 - 120 * q^48 - 113 * q^49 - 324 * q^50 - 56 * q^51 - 228 * q^52 - 616 * q^53 - 632 * q^54 - 128 * q^55 - 896 * q^56 - 120 * q^57 - 888 * q^58 + 52 * q^59 - 744 * q^60 - 520 * q^61 - 576 * q^62 + 210 * q^63 - 264 * q^64 - 92 * q^65 - 16 * q^66 - 296 * q^67 - 632 * q^68 + 112 * q^69 - 672 * q^70 - 268 * q^71 - 16 * q^72 + 34 * q^73 - 540 * q^74 - 4 * q^75 - 524 * q^76 - 44 * q^77 - 424 * q^78 + 882 * q^79 - 1616 * q^80 - 424 * q^81 - 1476 * q^82 + 1508 * q^83 - 1248 * q^84 + 384 * q^85 - 1192 * q^86 + 706 * q^87 - 456 * q^88 + 310 * q^89 - 736 * q^90 + 936 * q^91 - 304 * q^92 - 16 * q^93 - 96 * q^94 - 168 * q^95 + 120 * q^96 - 278 * q^97 + 416 * q^98 - 814 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(288))\)

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
288.3.b	\(\chi_{288}(271, \cdot)\)	288.3.b.a	1	1
		288.3.b.b	4
		288.3.b.c	4
288.3.e	\(\chi_{288}(161, \cdot)\)	288.3.e.a	2	1
		288.3.e.b	2
		288.3.e.c	2
		288.3.e.d	2
288.3.g	\(\chi_{288}(127, \cdot)\)	288.3.g.a	2	1
		288.3.g.b	2
		288.3.g.c	2
		288.3.g.d	4
288.3.h	\(\chi_{288}(17, \cdot)\)	288.3.h.a	8	1
288.3.j	\(\chi_{288}(89, \cdot)\)	None	0	2
288.3.m	\(\chi_{288}(55, \cdot)\)	None	0	2
288.3.n	\(\chi_{288}(113, \cdot)\)	288.3.n.a	44	2
288.3.o	\(\chi_{288}(31, \cdot)\)	288.3.o.a	4	2
		288.3.o.b	20
		288.3.o.c	24
288.3.q	\(\chi_{288}(65, \cdot)\)	288.3.q.a	24	2
		288.3.q.b	24
288.3.t	\(\chi_{288}(79, \cdot)\)	288.3.t.a	4	2
		288.3.t.b	40
288.3.u	\(\chi_{288}(19, \cdot)\)	288.3.u.a	28	4
		288.3.u.b	64
		288.3.u.c	64
288.3.x	\(\chi_{288}(53, \cdot)\)	288.3.x.a	64	4
		288.3.x.b	64
288.3.z	\(\chi_{288}(7, \cdot)\)	None	0	4
288.3.ba	\(\chi_{288}(41, \cdot)\)	None	0	4
288.3.bd	\(\chi_{288}(43, \cdot)\)	288.3.bd.a	752	8
288.3.be	\(\chi_{288}(5, \cdot)\)	288.3.be.a	752	8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(288))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(288)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)