Space of modular forms of level 864 and weight 2

• Label: 864.2
• Level: 864
• Weight: 2
• Dimension: 9056
• Nonzero newspaces: 18
• Newform subspaces: 48
• Sturm bound: 82944
• Trace bound: 29

Defining parameters

Level:	\( N \)	=	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 48 \)
Sturm bound:			\(82944\)
Trace bound:			\(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(864))\).

	Total	New	Old
Modular forms	21696	9376	12320
Cusp forms	19777	9056	10721
Eisenstein series	1919	320	1599

Trace form

9056 * q - 32 * q^2 - 36 * q^3 - 56 * q^4 - 32 * q^5 - 48 * q^6 - 42 * q^7 - 32 * q^8 - 72 * q^9 - 56 * q^10 - 26 * q^11 - 48 * q^12 - 56 * q^13 - 32 * q^14 - 36 * q^15 - 56 * q^16 - 24 * q^17 - 48 * q^18 - 50 * q^19 - 32 * q^20 - 48 * q^21 - 56 * q^22 - 34 * q^23 - 48 * q^24 - 100 * q^25 - 32 * q^26 - 36 * q^27 - 128 * q^28 - 48 * q^29 - 48 * q^30 - 50 * q^31 - 32 * q^32 - 120 * q^33 - 56 * q^34 - 14 * q^35 - 48 * q^36 - 40 * q^37 + 24 * q^38 - 36 * q^39 + 8 * q^40 - 16 * q^41 - 48 * q^42 - 26 * q^43 + 56 * q^44 - 48 * q^45 + 8 * q^46 + 6 * q^47 - 48 * q^48 + 4 * q^49 + 72 * q^50 - 18 * q^51 + 8 * q^52 + 16 * q^53 - 48 * q^54 - 60 * q^55 + 48 * q^56 - 48 * q^57 + 8 * q^58 + 46 * q^59 - 48 * q^60 + 24 * q^61 - 24 * q^62 + 24 * q^63 - 56 * q^64 + 100 * q^65 - 48 * q^66 + 22 * q^67 + 48 * q^69 - 56 * q^70 + 106 * q^71 - 48 * q^72 - 36 * q^73 - 32 * q^74 + 48 * q^75 - 56 * q^76 + 128 * q^77 - 48 * q^78 + 62 * q^79 - 96 * q^80 + 72 * q^81 - 208 * q^82 + 174 * q^83 - 48 * q^84 + 8 * q^85 - 136 * q^86 - 136 * q^88 + 24 * q^89 - 48 * q^90 + 106 * q^91 - 184 * q^92 - 48 * q^93 - 184 * q^94 + 170 * q^95 - 48 * q^96 - 108 * q^97 - 152 * q^98 - 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(864))\)

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
864.2.a	\(\chi_{864}(1, \cdot)\)	864.2.a.a	1	1
		864.2.a.b	1
		864.2.a.c	1
		864.2.a.d	1
		864.2.a.e	1
		864.2.a.f	1
		864.2.a.g	1
		864.2.a.h	1
		864.2.a.i	1
		864.2.a.j	1
		864.2.a.k	1
		864.2.a.l	1
		864.2.a.m	2
		864.2.a.n	2
864.2.c	\(\chi_{864}(863, \cdot)\)	864.2.c.a	8	1
		864.2.c.b	8
864.2.d	\(\chi_{864}(433, \cdot)\)	864.2.d.a	4	1
		864.2.d.b	4
		864.2.d.c	8
864.2.f	\(\chi_{864}(431, \cdot)\)	864.2.f.a	8	1
		864.2.f.b	8
864.2.i	\(\chi_{864}(289, \cdot)\)	864.2.i.a	2	2
		864.2.i.b	2
		864.2.i.c	4
		864.2.i.d	4
		864.2.i.e	4
		864.2.i.f	8
864.2.k	\(\chi_{864}(217, \cdot)\)	None	0	2
864.2.l	\(\chi_{864}(215, \cdot)\)	None	0	2
864.2.p	\(\chi_{864}(143, \cdot)\)	864.2.p.a	4	2
		864.2.p.b	16
864.2.r	\(\chi_{864}(145, \cdot)\)	864.2.r.a	4	2
		864.2.r.b	16
864.2.s	\(\chi_{864}(287, \cdot)\)	864.2.s.a	24	2
864.2.v	\(\chi_{864}(109, \cdot)\)	864.2.v.a	128	4
		864.2.v.b	128
864.2.w	\(\chi_{864}(107, \cdot)\)	864.2.w.a	128	4
		864.2.w.b	128
864.2.y	\(\chi_{864}(97, \cdot)\)	864.2.y.a	48	6
		864.2.y.b	54
		864.2.y.c	54
		864.2.y.d	60
864.2.z	\(\chi_{864}(71, \cdot)\)	None	0	4
864.2.bc	\(\chi_{864}(73, \cdot)\)	None	0	4
864.2.bf	\(\chi_{864}(49, \cdot)\)	864.2.bf.a	204	6
864.2.bh	\(\chi_{864}(47, \cdot)\)	864.2.bh.a	12	6
		864.2.bh.b	192
864.2.bi	\(\chi_{864}(95, \cdot)\)	864.2.bi.a	216	6
864.2.bk	\(\chi_{864}(37, \cdot)\)	864.2.bk.a	368	8
864.2.bn	\(\chi_{864}(35, \cdot)\)	864.2.bn.a	368	8
864.2.bo	\(\chi_{864}(25, \cdot)\)	None	0	12
864.2.br	\(\chi_{864}(23, \cdot)\)	None	0	12
864.2.bt	\(\chi_{864}(11, \cdot)\)	864.2.bt.a	3408	24
864.2.bu	\(\chi_{864}(13, \cdot)\)	864.2.bu.a	3408	24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(864))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(864)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 2}\)