Space of modular forms of level 288 and weight 5

• Label: 288.5
• Level: 288
• Weight: 5
• Dimension: 4059
• Nonzero newspaces: 12
• Sturm bound: 23040
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(23040\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(288))\).

	Total	New	Old
Modular forms	9472	4149	5323
Cusp forms	8960	4059	4901
Eisenstein series	512	90	422

Trace form

4059 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 36 * q^5 - 16 * q^6 - 10 * q^7 - 12 * q^8 - 24 * q^9 - 236 * q^10 + 84 * q^11 - 16 * q^12 + 220 * q^13 + 420 * q^14 - 174 * q^15 - 632 * q^16 - 630 * q^17 - 16 * q^18 + 678 * q^19 - 1212 * q^20 + 1200 * q^21 + 1880 * q^22 - 1158 * q^23 - 16 * q^24 - 1265 * q^25 - 2712 * q^26 - 1836 * q^27 - 2856 * q^28 - 2340 * q^29 + 112 * q^30 + 250 * q^31 + 1248 * q^32 + 3004 * q^33 + 3592 * q^34 - 4032 * q^35 + 12920 * q^36 + 4804 * q^37 + 7548 * q^38 - 1194 * q^39 - 21024 * q^40 - 11298 * q^41 - 23616 * q^42 + 3864 * q^43 - 35508 * q^44 - 8272 * q^45 - 8772 * q^46 + 6 * q^47 + 9864 * q^48 + 5539 * q^49 + 53340 * q^50 + 7192 * q^51 + 42396 * q^52 + 27036 * q^53 + 36328 * q^54 - 2528 * q^55 + 21120 * q^56 + 22824 * q^57 - 21672 * q^58 - 6540 * q^59 - 35688 * q^60 - 11876 * q^61 - 57696 * q^62 - 24654 * q^63 - 11400 * q^64 - 34836 * q^65 - 16 * q^66 + 15544 * q^67 + 14856 * q^68 - 17168 * q^69 + 49680 * q^70 + 19956 * q^71 - 16 * q^72 + 5882 * q^73 + 35364 * q^74 + 36092 * q^75 + 6644 * q^76 + 46260 * q^77 - 54280 * q^78 + 63218 * q^79 - 126288 * q^80 + 47288 * q^81 - 26436 * q^82 - 43692 * q^83 + 57888 * q^84 - 14392 * q^85 + 100200 * q^86 - 154862 * q^87 + 69048 * q^88 - 80130 * q^89 + 111584 * q^90 - 114072 * q^91 + 99216 * q^92 - 16 * q^93 + 1440 * q^94 - 3768 * q^95 - 25992 * q^96 + 40178 * q^97 - 67200 * q^98 + 103346 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(288))\)

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
288.5.b	\(\chi_{288}(271, \cdot)\)	288.5.b.a	1	1
		288.5.b.b	2
		288.5.b.c	8
		288.5.b.d	8
288.5.e	\(\chi_{288}(161, \cdot)\)	288.5.e.a	2	1
		288.5.e.b	2
		288.5.e.c	4
		288.5.e.d	4
		288.5.e.e	4
288.5.g	\(\chi_{288}(127, \cdot)\)	288.5.g.a	2	1
		288.5.g.b	2
		288.5.g.c	4
		288.5.g.d	4
		288.5.g.e	4
		288.5.g.f	4
288.5.h	\(\chi_{288}(17, \cdot)\)	288.5.h.a	16	1
288.5.j	\(\chi_{288}(89, \cdot)\)	None	0	2
288.5.m	\(\chi_{288}(55, \cdot)\)	None	0	2
288.5.n	\(\chi_{288}(113, \cdot)\)	288.5.n.a	92	2
288.5.o	\(\chi_{288}(31, \cdot)\)	288.5.o.a	48	2
		288.5.o.b	48
288.5.q	\(\chi_{288}(65, \cdot)\)	288.5.q.a	48	2
		288.5.q.b	48
288.5.t	\(\chi_{288}(79, \cdot)\)	288.5.t.a	4	2
		288.5.t.b	88
288.5.u	\(\chi_{288}(19, \cdot)\)	n/a	316	4
288.5.x	\(\chi_{288}(53, \cdot)\)	n/a	256	4
288.5.z	\(\chi_{288}(7, \cdot)\)	None	0	4
288.5.ba	\(\chi_{288}(41, \cdot)\)	None	0	4
288.5.bd	\(\chi_{288}(43, \cdot)\)	n/a	1520	8
288.5.be	\(\chi_{288}(5, \cdot)\)	n/a	1520	8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(288))\) into lower level spaces

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