Space of modular forms of level 288 and weight 8

• Label: 288.8
• Level: 288
• Weight: 8
• Dimension: 7137
• Nonzero newspaces: 12
• Sturm bound: 36864
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(36864\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(288))\).

	Total	New	Old
Modular forms	16384	7227	9157
Cusp forms	15872	7137	8735
Eisenstein series	512	90	422

Trace form

7137 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 290 * q^5 - 16 * q^6 + 678 * q^7 - 12 * q^8 - 24 * q^9 - 13036 * q^10 - 6 * q^11 - 16 * q^12 + 13606 * q^13 - 26204 * q^14 + 4362 * q^15 - 52792 * q^16 - 66106 * q^17 - 16 * q^18 + 121140 * q^19 + 81988 * q^20 - 4704 * q^21 - 374248 * q^22 - 434142 * q^23 - 16 * q^24 + 32767 * q^25 - 363992 * q^26 + 238032 * q^27 - 195496 * q^28 + 323638 * q^29 - 1040 * q^30 - 1161766 * q^31 + 535648 * q^32 - 269084 * q^33 - 201080 * q^34 + 816492 * q^35 - 730120 * q^36 + 2108966 * q^37 + 5109436 * q^38 + 146334 * q^39 - 2866336 * q^40 - 3794206 * q^41 - 5990976 * q^42 - 1139522 * q^43 - 1984756 * q^44 + 2210912 * q^45 + 8147388 * q^46 + 2586462 * q^47 + 10088712 * q^48 + 3865393 * q^49 + 326556 * q^50 - 1125980 * q^51 - 6236772 * q^52 - 13736130 * q^53 - 14891288 * q^54 - 4799288 * q^55 - 10509568 * q^56 - 720360 * q^57 + 16629912 * q^58 + 10005574 * q^59 + 17197080 * q^60 - 5728826 * q^61 - 18150816 * q^62 - 11485218 * q^63 + 16915512 * q^64 - 14576536 * q^65 - 16 * q^66 - 1164418 * q^67 - 9157688 * q^68 + 14060848 * q^69 - 8149488 * q^70 + 5269900 * q^71 - 16 * q^72 + 677598 * q^73 + 10931428 * q^74 - 2254012 * q^75 + 14443508 * q^76 - 39457084 * q^77 + 39347576 * q^78 - 5942886 * q^79 - 104949200 * q^80 - 9215800 * q^81 - 82802116 * q^82 + 43046454 * q^83 + 17056800 * q^84 + 6941676 * q^85 + 124258088 * q^86 - 83645306 * q^87 + 110752120 * q^88 - 25358550 * q^89 + 31733984 * q^90 + 16922112 * q^91 - 81318896 * q^92 - 16 * q^93 - 163612192 * q^94 + 171106312 * q^95 - 112869000 * q^96 + 7063342 * q^97 - 67942016 * q^98 + 33890246 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(288))\)

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
288.8.a	\(\chi_{288}(1, \cdot)\)	288.8.a.a	1	1
		288.8.a.b	1
		288.8.a.c	1
		288.8.a.d	1
		288.8.a.e	1
		288.8.a.f	2
		288.8.a.g	2
		288.8.a.h	2
		288.8.a.i	2
		288.8.a.j	2
		288.8.a.k	2
		288.8.a.l	2
		288.8.a.m	2
		288.8.a.n	2
		288.8.a.o	2
		288.8.a.p	2
		288.8.a.q	4
		288.8.a.r	4
288.8.c	\(\chi_{288}(287, \cdot)\)	288.8.c.a	12	1
		288.8.c.b	16
288.8.d	\(\chi_{288}(145, \cdot)\)	288.8.d.a	2	1
		288.8.d.b	6
		288.8.d.c	12
		288.8.d.d	14
288.8.f	\(\chi_{288}(143, \cdot)\)	288.8.f.a	28	1
288.8.i	\(\chi_{288}(97, \cdot)\)	n/a	168	2
288.8.k	\(\chi_{288}(73, \cdot)\)	None	0	2
288.8.l	\(\chi_{288}(71, \cdot)\)	None	0	2
288.8.p	\(\chi_{288}(47, \cdot)\)	n/a	164	2
288.8.r	\(\chi_{288}(49, \cdot)\)	n/a	164	2
288.8.s	\(\chi_{288}(95, \cdot)\)	n/a	168	2
288.8.v	\(\chi_{288}(37, \cdot)\)	n/a	556	4
288.8.w	\(\chi_{288}(35, \cdot)\)	n/a	448	4
288.8.y	\(\chi_{288}(23, \cdot)\)	None	0	4
288.8.bb	\(\chi_{288}(25, \cdot)\)	None	0	4
288.8.bc	\(\chi_{288}(13, \cdot)\)	n/a	2672	8
288.8.bf	\(\chi_{288}(11, \cdot)\)	n/a	2672	8

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(288))\) into lower level spaces

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