Space of modular forms of level 288 and weight 6

• Label: 288.6
• Level: 288
• Weight: 6
• Dimension: 5085
• Nonzero newspaces: 12
• Sturm bound: 27648
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(27648\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(288))\).

	Total	New	Old
Modular forms	11776	5175	6601
Cusp forms	11264	5085	6179
Eisenstein series	512	90	422

Trace form

5085 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 + 26 * q^5 - 16 * q^6 - 106 * q^7 - 12 * q^8 - 24 * q^9 - 236 * q^10 - 6 * q^11 - 16 * q^12 + 98 * q^13 + 2468 * q^14 + 474 * q^15 + 4168 * q^16 - 2210 * q^17 - 16 * q^18 - 4748 * q^19 - 7612 * q^20 + 3264 * q^21 - 12392 * q^22 + 12018 * q^23 - 16 * q^24 + 8175 * q^25 + 12968 * q^26 - 3744 * q^27 - 2216 * q^28 - 28174 * q^29 - 272 * q^30 + 21658 * q^31 - 18592 * q^32 + 8500 * q^33 - 6264 * q^34 - 4788 * q^35 - 68872 * q^36 - 15902 * q^37 + 138044 * q^38 + 22926 * q^39 + 211552 * q^40 + 57514 * q^41 + 60864 * q^42 + 30750 * q^43 - 142196 * q^44 - 72064 * q^45 - 190020 * q^46 - 33666 * q^47 - 224760 * q^48 - 49443 * q^49 - 260580 * q^50 - 9164 * q^51 + 91548 * q^52 + 29466 * q^53 + 230632 * q^54 + 147096 * q^55 + 544768 * q^56 - 7176 * q^57 + 305688 * q^58 + 16790 * q^59 - 97512 * q^60 - 69214 * q^61 - 541728 * q^62 + 127614 * q^63 - 49224 * q^64 + 116896 * q^65 - 16 * q^66 - 36706 * q^67 - 167608 * q^68 - 252752 * q^69 - 56304 * q^70 - 204004 * q^71 - 16 * q^72 + 134118 * q^73 + 213092 * q^74 - 159484 * q^75 + 255988 * q^76 + 215332 * q^77 + 527480 * q^78 - 717830 * q^79 + 290096 * q^80 + 537704 * q^81 - 571076 * q^82 + 1481574 * q^83 - 985056 * q^84 - 188060 * q^85 - 1173848 * q^86 + 554998 * q^87 - 646408 * q^88 - 445182 * q^89 + 284384 * q^90 - 733248 * q^91 + 1192208 * q^92 - 16 * q^93 + 1380448 * q^94 - 2044408 * q^95 + 1214328 * q^96 - 268666 * q^97 + 1518464 * q^98 - 730714 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(288))\)

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
288.6.a	\(\chi_{288}(1, \cdot)\)	288.6.a.a	1	1
		288.6.a.b	1
		288.6.a.c	1
		288.6.a.d	1
		288.6.a.e	1
		288.6.a.f	1
		288.6.a.g	1
		288.6.a.h	1
		288.6.a.i	1
		288.6.a.j	1
		288.6.a.k	1
		288.6.a.l	2
		288.6.a.m	2
		288.6.a.n	2
		288.6.a.o	2
		288.6.a.p	2
		288.6.a.q	2
		288.6.a.r	2
288.6.c	\(\chi_{288}(287, \cdot)\)	288.6.c.a	8	1
		288.6.c.b	12
288.6.d	\(\chi_{288}(145, \cdot)\)	288.6.d.a	2	1
		288.6.d.b	4
		288.6.d.c	8
		288.6.d.d	10
288.6.f	\(\chi_{288}(143, \cdot)\)	288.6.f.a	20	1
288.6.i	\(\chi_{288}(97, \cdot)\)	n/a	120	2
288.6.k	\(\chi_{288}(73, \cdot)\)	None	0	2
288.6.l	\(\chi_{288}(71, \cdot)\)	None	0	2
288.6.p	\(\chi_{288}(47, \cdot)\)	n/a	116	2
288.6.r	\(\chi_{288}(49, \cdot)\)	n/a	116	2
288.6.s	\(\chi_{288}(95, \cdot)\)	n/a	120	2
288.6.v	\(\chi_{288}(37, \cdot)\)	n/a	396	4
288.6.w	\(\chi_{288}(35, \cdot)\)	n/a	320	4
288.6.y	\(\chi_{288}(23, \cdot)\)	None	0	4
288.6.bb	\(\chi_{288}(25, \cdot)\)	None	0	4
288.6.bc	\(\chi_{288}(13, \cdot)\)	n/a	1904	8
288.6.bf	\(\chi_{288}(11, \cdot)\)	n/a	1904	8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(288))\) into lower level spaces

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