Space of modular forms of level 864 and weight 5

• Label: 864.5
• Level: 864
• Weight: 5
• Dimension: 36704
• Nonzero newspaces: 18
• Sturm bound: 207360
• Trace bound: 29

Defining parameters

Level:	\( N \)	=	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 18 \)
Sturm bound:			\(207360\)
Trace bound:			\(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(864))\).

	Total	New	Old
Modular forms	83904	37024	46880
Cusp forms	81984	36704	45280
Eisenstein series	1920	320	1600

Trace form

36704 * 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 - 22 * q^11 - 48 * q^12 - 56 * q^13 - 32 * q^14 - 36 * q^15 - 56 * q^16 + 80 * q^17 - 48 * q^18 - 746 * q^19 - 32 * q^20 - 48 * q^21 - 56 * q^22 - 26 * q^23 - 48 * q^24 + 1388 * q^25 - 32 * q^26 - 36 * q^27 - 128 * q^28 + 2080 * q^29 - 48 * q^30 - 170 * q^31 - 32 * q^32 - 120 * q^33 - 56 * q^34 - 2534 * q^35 - 48 * q^36 - 4216 * q^37 - 2552 * q^38 - 36 * q^39 + 13832 * q^40 + 8784 * q^41 - 48 * q^42 + 4438 * q^43 + 20824 * q^44 - 48 * q^45 + 5768 * q^46 - 34 * q^47 - 48 * q^48 - 6044 * q^49 - 28424 * q^50 - 522 * q^51 - 25336 * q^52 - 20192 * q^53 - 48 * q^54 - 8484 * q^55 - 22352 * q^56 - 27624 * q^57 + 3464 * q^58 - 14998 * q^59 - 48 * q^60 + 30600 * q^61 + 36456 * q^62 + 29724 * q^63 - 56 * q^64 + 92660 * q^65 - 48 * q^66 + 30166 * q^67 + 2016 * q^68 + 25680 * q^69 - 56 * q^70 - 14 * q^71 - 48 * q^72 - 13716 * q^73 - 32 * q^74 - 45060 * q^75 - 56 * q^76 - 113312 * q^77 - 48 * q^78 - 110890 * q^79 + 62368 * q^80 - 59544 * q^81 + 5072 * q^82 - 22 * q^83 - 48 * q^84 + 23240 * q^85 - 85208 * q^86 + 47196 * q^87 - 71176 * q^88 + 132336 * q^89 - 48 * q^90 + 89242 * q^91 - 79832 * q^92 - 48 * q^93 - 17752 * q^94 + 7482 * q^95 - 48 * q^96 - 12300 * q^97 + 76392 * q^98 - 36 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(864))\)

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
864.5.b	\(\chi_{864}(271, \cdot)\)	864.5.b.a	32	1
		864.5.b.b	32
864.5.e	\(\chi_{864}(161, \cdot)\)	864.5.e.a	8	1
		864.5.e.b	8
		864.5.e.c	8
		864.5.e.d	8
		864.5.e.e	8
		864.5.e.f	8
		864.5.e.g	16
864.5.g	\(\chi_{864}(703, \cdot)\)	864.5.g.a	16	1
		864.5.g.b	16
		864.5.g.c	16
		864.5.g.d	16
864.5.h	\(\chi_{864}(593, \cdot)\)	864.5.h.a	2	1
		864.5.h.b	2
		864.5.h.c	14
		864.5.h.d	14
		864.5.h.e	32
864.5.j	\(\chi_{864}(377, \cdot)\)	None	0	2
864.5.m	\(\chi_{864}(55, \cdot)\)	None	0	2
864.5.n	\(\chi_{864}(17, \cdot)\)	864.5.n.a	92	2
864.5.o	\(\chi_{864}(127, \cdot)\)	864.5.o.a	48	2
		864.5.o.b	48
864.5.q	\(\chi_{864}(449, \cdot)\)	864.5.q.a	48	2
		864.5.q.b	48
864.5.t	\(\chi_{864}(559, \cdot)\)	864.5.t.a	4	2
		864.5.t.b	88
864.5.u	\(\chi_{864}(163, \cdot)\)	n/a	1024	4
864.5.x	\(\chi_{864}(53, \cdot)\)	n/a	1024	4
864.5.ba	\(\chi_{864}(199, \cdot)\)	None	0	4
864.5.bb	\(\chi_{864}(89, \cdot)\)	None	0	4
864.5.bd	\(\chi_{864}(79, \cdot)\)	n/a	852	6
864.5.be	\(\chi_{864}(31, \cdot)\)	n/a	864	6
864.5.bg	\(\chi_{864}(65, \cdot)\)	n/a	864	6
864.5.bj	\(\chi_{864}(113, \cdot)\)	n/a	852	6
864.5.bl	\(\chi_{864}(19, \cdot)\)	n/a	1520	8
864.5.bm	\(\chi_{864}(125, \cdot)\)	n/a	1520	8
864.5.bp	\(\chi_{864}(7, \cdot)\)	None	0	12
864.5.bq	\(\chi_{864}(41, \cdot)\)	None	0	12
864.5.bs	\(\chi_{864}(5, \cdot)\)	n/a	13776	24
864.5.bv	\(\chi_{864}(43, \cdot)\)	n/a	13776	24

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(864))\) into lower level spaces

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