Space of modular forms of level 1152 and weight 3

• Label: 1152.3
• Level: 1152
• Weight: 3
• Dimension: 32616
• Nonzero newspaces: 20
• Sturm bound: 221184
• Trace bound: 33

Defining parameters

Level:	\( N \)	=	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(221184\)
Trace bound:			\(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1152))\).

	Total	New	Old
Modular forms	75008	33048	41960
Cusp forms	72448	32616	39832
Eisenstein series	2560	432	2128

Trace form

32616 * q - 48 * q^2 - 48 * q^3 - 48 * q^4 - 48 * q^5 - 64 * q^6 - 36 * q^7 - 48 * q^8 - 80 * q^9 - 144 * q^10 - 36 * q^11 - 64 * q^12 - 48 * q^13 - 48 * q^14 - 48 * q^15 - 48 * q^16 - 72 * q^17 - 64 * q^18 - 108 * q^19 - 48 * q^20 - 64 * q^21 - 48 * q^22 + 28 * q^23 - 64 * q^24 + 36 * q^25 - 48 * q^26 - 48 * q^27 - 144 * q^28 - 16 * q^29 - 64 * q^30 - 40 * q^31 - 48 * q^32 - 128 * q^33 - 48 * q^34 - 132 * q^35 - 64 * q^36 - 240 * q^37 - 48 * q^38 - 48 * q^39 - 48 * q^40 - 220 * q^41 - 64 * q^42 - 132 * q^43 - 48 * q^44 - 64 * q^45 - 144 * q^46 - 48 * q^47 - 64 * q^48 - 268 * q^49 - 672 * q^50 - 48 * q^51 - 1104 * q^52 - 368 * q^53 - 64 * q^54 - 364 * q^55 - 832 * q^56 - 80 * q^57 - 768 * q^58 - 164 * q^59 - 64 * q^60 - 176 * q^61 - 144 * q^62 - 48 * q^63 + 48 * q^64 + 80 * q^65 - 64 * q^66 + 124 * q^67 + 432 * q^68 - 136 * q^69 + 1296 * q^70 + 220 * q^71 - 64 * q^72 + 460 * q^73 + 1184 * q^74 - 248 * q^75 + 1616 * q^76 - 188 * q^77 - 64 * q^78 - 544 * q^79 + 768 * q^80 - 992 * q^81 - 144 * q^82 - 1476 * q^83 - 64 * q^84 - 808 * q^85 - 48 * q^86 - 944 * q^87 - 48 * q^88 - 1212 * q^89 - 64 * q^90 - 684 * q^91 - 48 * q^92 - 256 * q^93 - 48 * q^94 - 24 * q^95 - 64 * q^96 + 288 * q^97 - 48 * q^98 + 464 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1152))\)

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
1152.3.b	\(\chi_{1152}(703, \cdot)\)	1152.3.b.a	2	1
		1152.3.b.b	2
		1152.3.b.c	2
		1152.3.b.d	2
		1152.3.b.e	4
		1152.3.b.f	4
		1152.3.b.g	4
		1152.3.b.h	4
		1152.3.b.i	8
		1152.3.b.j	8
1152.3.e	\(\chi_{1152}(1025, \cdot)\)	1152.3.e.a	4	1
		1152.3.e.b	4
		1152.3.e.c	4
		1152.3.e.d	4
		1152.3.e.e	4
		1152.3.e.f	4
		1152.3.e.g	4
		1152.3.e.h	4
1152.3.g	\(\chi_{1152}(127, \cdot)\)	1152.3.g.a	4	1
		1152.3.g.b	4
		1152.3.g.c	8
		1152.3.g.d	8
		1152.3.g.e	8
		1152.3.g.f	8
1152.3.h	\(\chi_{1152}(449, \cdot)\)	1152.3.h.a	4	1
		1152.3.h.b	4
		1152.3.h.c	4
		1152.3.h.d	4
		1152.3.h.e	8
		1152.3.h.f	8
1152.3.j	\(\chi_{1152}(161, \cdot)\)	1152.3.j.a	32	2
		1152.3.j.b	32
1152.3.m	\(\chi_{1152}(415, \cdot)\)	1152.3.m.a	6	2
		1152.3.m.b	6
		1152.3.m.c	16
		1152.3.m.d	16
		1152.3.m.e	16
		1152.3.m.f	16
1152.3.n	\(\chi_{1152}(65, \cdot)\)	n/a	192	2
1152.3.o	\(\chi_{1152}(511, \cdot)\)	n/a	192	2
1152.3.q	\(\chi_{1152}(257, \cdot)\)	n/a	192	2
1152.3.t	\(\chi_{1152}(319, \cdot)\)	n/a	192	2
1152.3.u	\(\chi_{1152}(271, \cdot)\)	n/a	156	4
1152.3.x	\(\chi_{1152}(17, \cdot)\)	n/a	128	4
1152.3.z	\(\chi_{1152}(31, \cdot)\)	n/a	368	4
1152.3.ba	\(\chi_{1152}(353, \cdot)\)	n/a	368	4
1152.3.bc	\(\chi_{1152}(89, \cdot)\)	None	0	8
1152.3.bf	\(\chi_{1152}(55, \cdot)\)	None	0	8
1152.3.bh	\(\chi_{1152}(79, \cdot)\)	n/a	752	8
1152.3.bi	\(\chi_{1152}(113, \cdot)\)	n/a	752	8
1152.3.bk	\(\chi_{1152}(19, \cdot)\)	n/a	2544	16
1152.3.bn	\(\chi_{1152}(53, \cdot)\)	n/a	2048	16
1152.3.bo	\(\chi_{1152}(7, \cdot)\)	None	0	16
1152.3.br	\(\chi_{1152}(41, \cdot)\)	None	0	16
1152.3.bt	\(\chi_{1152}(5, \cdot)\)	n/a	12224	32
1152.3.bu	\(\chi_{1152}(43, \cdot)\)	n/a	12224	32

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1152))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1152)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 21}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 14}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 2}\)