Space of modular forms of level 288 and weight 2

• Label: 288.2
• Level: 288
• Weight: 2
• Dimension: 981
• Nonzero newspaces: 12
• Newform subspaces: 28
• Sturm bound: 9216
• Trace bound: 17

Defining parameters

Level:	\( N \)	=	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 28 \)
Sturm bound:			\(9216\)
Trace bound:			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(288))\).

	Total	New	Old
Modular forms	2560	1071	1489
Cusp forms	2049	981	1068
Eisenstein series	511	90	421

Trace form

981 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 14 * q^5 - 16 * q^6 - 10 * q^7 - 12 * q^8 - 24 * q^9 - 28 * q^10 - 6 * q^11 - 16 * q^12 - 6 * q^13 + 4 * q^14 - 6 * q^15 + 8 * q^16 + 14 * q^17 - 16 * q^18 - 12 * q^19 + 4 * q^20 + 18 * q^23 - 16 * q^24 + 15 * q^25 - 32 * q^26 - 56 * q^28 + 10 * q^29 - 32 * q^30 + 26 * q^31 - 32 * q^32 - 44 * q^33 - 24 * q^34 + 12 * q^35 - 40 * q^36 - 70 * q^37 - 116 * q^38 - 18 * q^39 - 128 * q^40 - 70 * q^41 - 96 * q^42 - 34 * q^43 - 148 * q^44 - 64 * q^45 - 132 * q^46 - 66 * q^47 - 120 * q^48 - 75 * q^49 - 180 * q^50 - 44 * q^51 - 132 * q^52 - 78 * q^53 - 104 * q^54 - 72 * q^55 - 160 * q^56 - 72 * q^57 - 144 * q^58 - 74 * q^59 - 72 * q^60 - 6 * q^61 - 48 * q^62 - 66 * q^63 - 72 * q^64 - 112 * q^65 - 16 * q^66 - 34 * q^67 - 56 * q^68 - 80 * q^69 - 24 * q^70 - 68 * q^71 - 16 * q^72 - 10 * q^73 + 4 * q^74 - 124 * q^75 - 12 * q^76 - 28 * q^77 + 8 * q^78 - 70 * q^79 + 112 * q^80 - 88 * q^81 + 124 * q^82 - 186 * q^83 + 96 * q^84 + 20 * q^85 + 176 * q^86 - 170 * q^87 + 152 * q^88 - 78 * q^89 + 128 * q^90 - 192 * q^91 + 256 * q^92 - 16 * q^93 + 160 * q^94 - 248 * q^95 + 120 * q^96 - 74 * q^97 + 208 * q^98 - 154 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)

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
288.2.a	\(\chi_{288}(1, \cdot)\)	288.2.a.a	1	1
		288.2.a.b	1
		288.2.a.c	1
		288.2.a.d	1
		288.2.a.e	1
288.2.c	\(\chi_{288}(287, \cdot)\)	288.2.c.a	4	1
288.2.d	\(\chi_{288}(145, \cdot)\)	288.2.d.a	2	1
		288.2.d.b	2
288.2.f	\(\chi_{288}(143, \cdot)\)	288.2.f.a	4	1
288.2.i	\(\chi_{288}(97, \cdot)\)	288.2.i.a	2	2
		288.2.i.b	2
		288.2.i.c	4
		288.2.i.d	4
		288.2.i.e	4
		288.2.i.f	8
288.2.k	\(\chi_{288}(73, \cdot)\)	None	0	2
288.2.l	\(\chi_{288}(71, \cdot)\)	None	0	2
288.2.p	\(\chi_{288}(47, \cdot)\)	288.2.p.a	4	2
		288.2.p.b	16
288.2.r	\(\chi_{288}(49, \cdot)\)	288.2.r.a	4	2
		288.2.r.b	16
288.2.s	\(\chi_{288}(95, \cdot)\)	288.2.s.a	24	2
288.2.v	\(\chi_{288}(37, \cdot)\)	288.2.v.a	4	4
		288.2.v.b	8
		288.2.v.c	32
		288.2.v.d	32
288.2.w	\(\chi_{288}(35, \cdot)\)	288.2.w.a	32	4
		288.2.w.b	32
288.2.y	\(\chi_{288}(23, \cdot)\)	None	0	4
288.2.bb	\(\chi_{288}(25, \cdot)\)	None	0	4
288.2.bc	\(\chi_{288}(13, \cdot)\)	288.2.bc.a	368	8
288.2.bf	\(\chi_{288}(11, \cdot)\)	288.2.bf.a	368	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(288))\) into lower level spaces

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