Space of modular forms of level 288 and weight 9

• Label: 288.9
• Level: 288
• Weight: 9
• Dimension: 8163
• Nonzero newspaces: 12
• Sturm bound: 41472
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(41472\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(288))\).

	Total	New	Old
Modular forms	18688	8253	10435
Cusp forms	18176	8163	10013
Eisenstein series	512	90	422

Trace form

8163 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 + 324 * q^5 - 16 * q^6 - 10 * q^7 - 12 * q^8 - 24 * q^9 + 34964 * q^10 - 19788 * q^11 - 16 * q^12 + 79940 * q^13 + 145572 * q^14 - 13134 * q^15 - 278392 * q^16 - 71910 * q^17 - 16 * q^18 - 167578 * q^19 + 689988 * q^20 + 683376 * q^21 + 6040 * q^22 + 845562 * q^23 - 16 * q^24 - 1875665 * q^25 + 1682088 * q^26 + 25524 * q^27 - 1807656 * q^28 + 3864132 * q^29 + 2032 * q^30 - 491014 * q^31 + 2420448 * q^32 - 2753636 * q^33 + 4139272 * q^34 - 1279872 * q^35 - 2470792 * q^36 - 15893716 * q^37 - 18983172 * q^38 + 3838134 * q^39 + 47218656 * q^40 + 17716686 * q^41 + 1109184 * q^42 - 8174536 * q^43 - 85437876 * q^44 - 27624592 * q^45 - 35372100 * q^46 + 6 * q^47 + 43639944 * q^48 + 32609611 * q^49 + 137158620 * q^50 + 15120952 * q^51 + 8613276 * q^52 - 41136444 * q^53 - 85444760 * q^54 - 1562528 * q^55 - 149374848 * q^56 - 24081816 * q^57 + 9953688 * q^58 - 22469388 * q^59 + 171189912 * q^60 + 88460228 * q^61 - 159027936 * q^62 + 69695346 * q^63 + 27135096 * q^64 + 6834684 * q^65 - 16 * q^66 + 96826744 * q^67 - 1540344 * q^68 - 144659984 * q^69 - 167238960 * q^70 - 79832076 * q^71 - 16 * q^72 - 127646678 * q^73 + 28015140 * q^74 + 205180412 * q^75 + 201789940 * q^76 + 90498420 * q^77 - 299591560 * q^78 - 172741134 * q^79 + 622161072 * q^80 - 459284104 * q^81 - 92032836 * q^82 + 316489908 * q^83 - 689231328 * q^84 - 114420072 * q^85 - 841156440 * q^86 + 639208498 * q^87 + 311519928 * q^88 - 218700786 * q^89 + 873269984 * q^90 - 1104572184 * q^91 + 1563063696 * q^92 - 16 * q^93 + 520293024 * q^94 - 2343768 * q^95 - 468840840 * q^96 + 128539138 * q^97 - 1683767040 * q^98 + 1488949106 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(288))\)

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
288.9.b	\(\chi_{288}(271, \cdot)\)	288.9.b.a	1	1
		288.9.b.b	6
		288.9.b.c	16
		288.9.b.d	16
288.9.e	\(\chi_{288}(161, \cdot)\)	288.9.e.a	2	1
		288.9.e.b	2
		288.9.e.c	4
		288.9.e.d	8
		288.9.e.e	8
		288.9.e.f	8
288.9.g	\(\chi_{288}(127, \cdot)\)	288.9.g.a	4	1
		288.9.g.b	4
		288.9.g.c	8
		288.9.g.d	8
		288.9.g.e	8
		288.9.g.f	8
288.9.h	\(\chi_{288}(17, \cdot)\)	288.9.h.a	32	1
288.9.j	\(\chi_{288}(89, \cdot)\)	None	0	2
288.9.m	\(\chi_{288}(55, \cdot)\)	None	0	2
288.9.n	\(\chi_{288}(113, \cdot)\)	n/a	188	2
288.9.o	\(\chi_{288}(31, \cdot)\)	n/a	192	2
288.9.q	\(\chi_{288}(65, \cdot)\)	n/a	192	2
288.9.t	\(\chi_{288}(79, \cdot)\)	n/a	188	2
288.9.u	\(\chi_{288}(19, \cdot)\)	n/a	636	4
288.9.x	\(\chi_{288}(53, \cdot)\)	n/a	512	4
288.9.z	\(\chi_{288}(7, \cdot)\)	None	0	4
288.9.ba	\(\chi_{288}(41, \cdot)\)	None	0	4
288.9.bd	\(\chi_{288}(43, \cdot)\)	n/a	3056	8
288.9.be	\(\chi_{288}(5, \cdot)\)	n/a	3056	8

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

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(288))\) into lower level spaces

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