Space of modular forms of level 288 and weight 10

• Label: 288.10
• Level: 288
• Weight: 10
• Dimension: 9189
• Nonzero newspaces: 12
• Sturm bound: 46080
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(46080\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(288))\).

	Total	New	Old
Modular forms	20992	9279	11713
Cusp forms	20480	9189	11291
Eisenstein series	512	90	422

Trace form

9189 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 + 706 * q^5 - 16 * q^6 - 4810 * q^7 - 12 * q^8 - 24 * q^9 - 45036 * q^10 - 6 * q^11 - 16 * q^12 - 108470 * q^13 + 221092 * q^14 + 39354 * q^15 + 566088 * q^16 + 318638 * q^17 - 16 * q^18 - 961804 * q^19 + 1809988 * q^20 - 1268352 * q^21 - 270568 * q^22 - 161838 * q^23 - 16 * q^24 + 1387215 * q^25 + 1052968 * q^26 - 6325056 * q^27 + 10895704 * q^28 + 12696922 * q^29 - 4112 * q^30 + 34050330 * q^31 - 14720672 * q^32 - 19287404 * q^33 + 19270536 * q^34 - 38240628 * q^35 + 53462264 * q^36 + 56689290 * q^37 - 153886916 * q^38 - 36097746 * q^39 - 206664608 * q^40 + 41440154 * q^41 + 246074304 * q^42 + 69762142 * q^43 + 162425228 * q^44 - 44242624 * q^45 - 339409476 * q^46 - 202619586 * q^47 - 440619000 * q^48 - 22261755 * q^49 + 436309020 * q^50 + 117278356 * q^51 + 734963100 * q^52 + 579384066 * q^53 + 206015464 * q^54 - 279462024 * q^55 - 1210837504 * q^56 - 299386824 * q^57 - 448034664 * q^58 + 436678006 * q^59 + 1193643288 * q^60 + 1026616522 * q^61 - 908468256 * q^62 - 110705346 * q^63 - 715478856 * q^64 + 378075056 * q^65 - 16 * q^66 + 302128478 * q^67 + 1269417544 * q^68 - 680879696 * q^69 + 1332494736 * q^70 - 1033660292 * q^71 - 16 * q^72 + 304374742 * q^73 - 2309233820 * q^74 + 895706756 * q^75 - 428646412 * q^76 + 1590420068 * q^77 + 2023944056 * q^78 + 5580385338 * q^79 - 5441099984 * q^80 - 1659168472 * q^81 + 4838481724 * q^82 - 11153626746 * q^83 + 6148771872 * q^84 - 2168167500 * q^85 - 3264349144 * q^86 + 8522348182 * q^87 - 8036618248 * q^88 + 1946266194 * q^89 - 7222410016 * q^90 + 4527681600 * q^91 + 7767783184 * q^92 - 16 * q^93 + 5879687008 * q^94 - 19382208248 * q^95 + 10366581624 * q^96 - 1665292458 * q^97 + 9338246272 * q^98 + 4666903526 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(288))\)

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
288.10.a	\(\chi_{288}(1, \cdot)\)	288.10.a.a	1	1
		288.10.a.b	1
		288.10.a.c	1
		288.10.a.d	2
		288.10.a.e	2
		288.10.a.f	2
		288.10.a.g	2
		288.10.a.h	2
		288.10.a.i	2
		288.10.a.j	2
		288.10.a.k	2
		288.10.a.l	2
		288.10.a.m	2
		288.10.a.n	3
		288.10.a.o	3
		288.10.a.p	4
		288.10.a.q	4
		288.10.a.r	4
		288.10.a.s	4
288.10.c	\(\chi_{288}(287, \cdot)\)	288.10.c.a	16	1
		288.10.c.b	20
288.10.d	\(\chi_{288}(145, \cdot)\)	288.10.d.a	2	1
		288.10.d.b	8
		288.10.d.c	16
		288.10.d.d	18
288.10.f	\(\chi_{288}(143, \cdot)\)	288.10.f.a	36	1
288.10.i	\(\chi_{288}(97, \cdot)\)	n/a	216	2
288.10.k	\(\chi_{288}(73, \cdot)\)	None	0	2
288.10.l	\(\chi_{288}(71, \cdot)\)	None	0	2
288.10.p	\(\chi_{288}(47, \cdot)\)	n/a	212	2
288.10.r	\(\chi_{288}(49, \cdot)\)	n/a	212	2
288.10.s	\(\chi_{288}(95, \cdot)\)	n/a	216	2
288.10.v	\(\chi_{288}(37, \cdot)\)	n/a	716	4
288.10.w	\(\chi_{288}(35, \cdot)\)	n/a	576	4
288.10.y	\(\chi_{288}(23, \cdot)\)	None	0	4
288.10.bb	\(\chi_{288}(25, \cdot)\)	None	0	4
288.10.bc	\(\chi_{288}(13, \cdot)\)	n/a	3440	8
288.10.bf	\(\chi_{288}(11, \cdot)\)	n/a	3440	8

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(288))\) into lower level spaces

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