Space of modular forms of level 288 and weight 4

• Label: 288.4
• Level: 288
• Weight: 4
• Dimension: 3033
• Nonzero newspaces: 12
• Sturm bound: 18432
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(18432\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(288))\).

	Total	New	Old
Modular forms	7168	3123	4045
Cusp forms	6656	3033	3623
Eisenstein series	512	90	422

Trace form

3033 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 10 * q^5 - 16 * q^6 + 6 * q^7 - 12 * q^8 - 24 * q^9 + 84 * q^10 - 6 * q^11 - 16 * q^12 - 130 * q^13 - 220 * q^14 + 42 * q^15 - 312 * q^16 + 118 * q^17 - 16 * q^18 - 76 * q^19 + 68 * q^20 - 288 * q^21 + 184 * q^22 + 66 * q^23 - 16 * q^24 - 353 * q^25 + 8 * q^26 - 144 * q^27 + 344 * q^28 + 14 * q^29 - 80 * q^30 - 678 * q^31 + 608 * q^32 + 388 * q^33 + 520 * q^34 - 468 * q^35 - 2056 * q^36 - 1218 * q^37 - 3844 * q^38 - 258 * q^39 - 1696 * q^40 + 754 * q^41 + 1344 * q^42 + 1662 * q^43 + 4108 * q^44 + 1952 * q^45 + 4284 * q^46 + 1182 * q^47 + 4872 * q^48 + 1801 * q^49 + 4956 * q^50 + 580 * q^51 + 924 * q^52 + 2070 * q^53 + 424 * q^54 + 232 * q^55 - 2816 * q^56 - 3624 * q^57 - 4872 * q^58 - 1690 * q^59 - 6120 * q^60 - 4642 * q^61 - 4320 * q^62 - 738 * q^63 + 4920 * q^64 + 1624 * q^65 - 16 * q^66 + 1214 * q^67 + 1736 * q^68 + 4144 * q^69 + 1392 * q^70 + 2348 * q^71 - 16 * q^72 - 4114 * q^73 - 3484 * q^74 + 1988 * q^75 - 5132 * q^76 + 1924 * q^77 + 5048 * q^78 - 13478 * q^79 + 8240 * q^80 - 3064 * q^81 + 7484 * q^82 - 10986 * q^83 + 4128 * q^84 + 796 * q^85 - 1976 * q^86 - 794 * q^87 - 5000 * q^88 - 294 * q^89 - 9376 * q^90 + 15744 * q^91 - 15088 * q^92 - 16 * q^93 - 5152 * q^94 + 25352 * q^95 - 12936 * q^96 + 8286 * q^97 - 13120 * q^98 + 14726 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(288))\)

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
288.4.a	\(\chi_{288}(1, \cdot)\)	288.4.a.a	1	1
		288.4.a.b	1
		288.4.a.c	1
		288.4.a.d	1
		288.4.a.e	1
		288.4.a.f	1
		288.4.a.g	1
		288.4.a.h	1
		288.4.a.i	1
		288.4.a.j	1
		288.4.a.k	1
		288.4.a.l	2
		288.4.a.m	2
288.4.c	\(\chi_{288}(287, \cdot)\)	288.4.c.a	4	1
		288.4.c.b	8
288.4.d	\(\chi_{288}(145, \cdot)\)	288.4.d.a	2	1
		288.4.d.b	2
		288.4.d.c	4
		288.4.d.d	6
288.4.f	\(\chi_{288}(143, \cdot)\)	288.4.f.a	12	1
288.4.i	\(\chi_{288}(97, \cdot)\)	288.4.i.a	8	2
		288.4.i.b	12
		288.4.i.c	16
		288.4.i.d	18
		288.4.i.e	18
288.4.k	\(\chi_{288}(73, \cdot)\)	None	0	2
288.4.l	\(\chi_{288}(71, \cdot)\)	None	0	2
288.4.p	\(\chi_{288}(47, \cdot)\)	288.4.p.a	4	2
		288.4.p.b	64
288.4.r	\(\chi_{288}(49, \cdot)\)	288.4.r.a	68	2
288.4.s	\(\chi_{288}(95, \cdot)\)	288.4.s.a	72	2
288.4.v	\(\chi_{288}(37, \cdot)\)	n/a	236	4
288.4.w	\(\chi_{288}(35, \cdot)\)	n/a	192	4
288.4.y	\(\chi_{288}(23, \cdot)\)	None	0	4
288.4.bb	\(\chi_{288}(25, \cdot)\)	None	0	4
288.4.bc	\(\chi_{288}(13, \cdot)\)	n/a	1136	8
288.4.bf	\(\chi_{288}(11, \cdot)\)	n/a	1136	8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(288))\) into lower level spaces

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