Space of modular forms of level 288 and weight 7

• Label: 288.7
• Level: 288
• Weight: 7
• Dimension: 6111
• Nonzero newspaces: 12
• Sturm bound: 32256
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(32256\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(288))\).

	Total	New	Old
Modular forms	14080	6201	7879
Cusp forms	13568	6111	7457
Eisenstein series	512	90	422

Trace form

6111 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 + 32 * q^5 - 16 * q^6 - 10 * q^7 - 12 * q^8 - 24 * q^9 + 2964 * q^10 + 1348 * q^11 - 16 * q^12 - 4224 * q^13 - 8540 * q^14 - 1470 * q^15 + 14088 * q^16 + 30290 * q^17 - 16 * q^18 - 3962 * q^19 - 14012 * q^20 - 32112 * q^21 - 19560 * q^22 + 13114 * q^23 - 16 * q^24 + 97471 * q^25 + 5288 * q^26 + 34308 * q^27 + 85464 * q^28 - 32960 * q^29 + 496 * q^30 - 122502 * q^31 - 58912 * q^32 + 8236 * q^33 - 139256 * q^34 + 337248 * q^35 + 291704 * q^36 - 95736 * q^37 - 972676 * q^38 - 125754 * q^39 - 141600 * q^40 + 534 * q^41 + 686784 * q^42 + 413416 * q^43 + 1464268 * q^44 + 515600 * q^45 + 591804 * q^46 + 6 * q^47 - 699000 * q^48 - 440777 * q^49 - 2352804 * q^50 - 380696 * q^51 - 2335332 * q^52 - 486272 * q^53 - 348056 * q^54 - 62528 * q^55 + 2512256 * q^56 + 1755336 * q^57 + 4411032 * q^58 + 443060 * q^59 + 872856 * q^60 - 1224864 * q^61 - 3162720 * q^62 - 275310 * q^63 - 1533960 * q^64 + 1392308 * q^65 - 16 * q^66 - 726632 * q^67 + 382088 * q^68 + 1688944 * q^69 - 676272 * q^70 - 267020 * q^71 - 16 * q^72 + 101202 * q^73 - 661596 * q^74 - 2607364 * q^75 + 873972 * q^76 - 4271980 * q^77 - 4734856 * q^78 + 2914930 * q^79 + 1798064 * q^80 + 528152 * q^81 + 12526524 * q^82 - 7974332 * q^83 + 5971488 * q^84 + 2301904 * q^85 + 489640 * q^86 + 5397730 * q^87 - 6536136 * q^88 - 869818 * q^89 - 11466016 * q^90 + 11875368 * q^91 - 20751728 * q^92 - 16 * q^93 - 7455456 * q^94 - 93768 * q^95 + 3708024 * q^96 + 1438458 * q^97 + 22770688 * q^98 - 15989614 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(288))\)

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
288.7.b	\(\chi_{288}(271, \cdot)\)	288.7.b.a	1	1
		288.7.b.b	4
		288.7.b.c	12
		288.7.b.d	12
288.7.e	\(\chi_{288}(161, \cdot)\)	288.7.e.a	2	1
		288.7.e.b	2
		288.7.e.c	2
		288.7.e.d	2
		288.7.e.e	4
		288.7.e.f	4
		288.7.e.g	4
		288.7.e.h	4
288.7.g	\(\chi_{288}(127, \cdot)\)	288.7.g.a	2	1
		288.7.g.b	4
		288.7.g.c	4
		288.7.g.d	6
		288.7.g.e	6
		288.7.g.f	8
288.7.h	\(\chi_{288}(17, \cdot)\)	288.7.h.a	24	1
288.7.j	\(\chi_{288}(89, \cdot)\)	None	0	2
288.7.m	\(\chi_{288}(55, \cdot)\)	None	0	2
288.7.n	\(\chi_{288}(113, \cdot)\)	n/a	140	2
288.7.o	\(\chi_{288}(31, \cdot)\)	n/a	144	2
288.7.q	\(\chi_{288}(65, \cdot)\)	n/a	144	2
288.7.t	\(\chi_{288}(79, \cdot)\)	n/a	140	2
288.7.u	\(\chi_{288}(19, \cdot)\)	n/a	476	4
288.7.x	\(\chi_{288}(53, \cdot)\)	n/a	384	4
288.7.z	\(\chi_{288}(7, \cdot)\)	None	0	4
288.7.ba	\(\chi_{288}(41, \cdot)\)	None	0	4
288.7.bd	\(\chi_{288}(43, \cdot)\)	n/a	2288	8
288.7.be	\(\chi_{288}(5, \cdot)\)	n/a	2288	8

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(288))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(288)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 15}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 10}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 9}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)