Space of modular forms of level 1152 and weight 4

• Label: 1152.4
• Level: 1152
• Weight: 4
• Dimension: 49032
• Nonzero newspaces: 20
• Sturm bound: 294912
• Trace bound: 33

Defining parameters

Level:	\( N \)	=	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(294912\)
Trace bound:			\(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1152))\).

	Total	New	Old
Modular forms	111872	49464	62408
Cusp forms	109312	49032	60280
Eisenstein series	2560	432	2128

Trace form

49032 * 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 - 364 * q^23 - 64 * q^24 - 236 * q^25 - 48 * q^26 - 48 * q^27 - 144 * q^28 + 352 * q^29 - 64 * q^30 + 712 * q^31 - 48 * q^32 - 128 * q^33 - 48 * q^34 + 420 * q^35 - 64 * q^36 - 128 * q^37 - 48 * q^38 - 48 * q^39 - 48 * q^40 - 1004 * q^41 - 64 * q^42 - 844 * q^43 - 48 * q^44 - 64 * q^45 - 144 * q^46 - 24 * q^47 - 64 * q^48 + 1300 * q^49 + 5664 * q^50 - 48 * q^51 + 6576 * q^52 + 1456 * q^53 - 64 * q^54 + 180 * q^55 - 832 * q^56 - 80 * q^57 - 4800 * q^58 - 1412 * q^59 - 64 * q^60 - 3696 * q^61 - 5904 * q^62 - 48 * q^63 - 12240 * q^64 - 3952 * q^65 - 64 * q^66 - 2076 * q^67 - 4176 * q^68 + 152 * q^69 - 4080 * q^70 - 260 * q^71 - 64 * q^72 + 1548 * q^73 + 5216 * q^74 + 952 * q^75 + 11856 * q^76 + 7876 * q^77 - 64 * q^78 + 11288 * q^79 + 9984 * q^80 + 7264 * q^81 - 144 * q^82 + 7284 * q^83 - 64 * q^84 + 2392 * q^85 - 48 * q^86 - 2624 * q^87 - 48 * q^88 - 10236 * q^89 - 64 * q^90 - 10908 * q^91 - 48 * q^92 - 8608 * q^93 - 48 * q^94 - 18288 * q^95 - 64 * q^96 - 17952 * q^97 - 48 * q^98 - 10672 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1152))\)

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
1152.4.a	\(\chi_{1152}(1, \cdot)\)	1152.4.a.a	1	1
		1152.4.a.b	1
		1152.4.a.c	1
		1152.4.a.d	1
		1152.4.a.e	1
		1152.4.a.f	1
		1152.4.a.g	1
		1152.4.a.h	1
		1152.4.a.i	1
		1152.4.a.j	1
		1152.4.a.k	1
		1152.4.a.l	1
		1152.4.a.m	2
		1152.4.a.n	2
		1152.4.a.o	2
		1152.4.a.p	2
		1152.4.a.q	2
		1152.4.a.r	2
		1152.4.a.s	2
		1152.4.a.t	2
		1152.4.a.u	2
		1152.4.a.v	2
		1152.4.a.w	2
		1152.4.a.x	2
		1152.4.a.y	3
		1152.4.a.z	3
		1152.4.a.ba	3
		1152.4.a.bb	3
		1152.4.a.bc	3
		1152.4.a.bd	3
		1152.4.a.be	3
		1152.4.a.bf	3
1152.4.c	\(\chi_{1152}(1151, \cdot)\)	1152.4.c.a	12	1
		1152.4.c.b	12
		1152.4.c.c	12
		1152.4.c.d	12
1152.4.d	\(\chi_{1152}(577, \cdot)\)	1152.4.d.a	2	1
		1152.4.d.b	2
		1152.4.d.c	2
		1152.4.d.d	2
		1152.4.d.e	2
		1152.4.d.f	2
		1152.4.d.g	2
		1152.4.d.h	2
		1152.4.d.i	4
		1152.4.d.j	4
		1152.4.d.k	4
		1152.4.d.l	4
		1152.4.d.m	4
		1152.4.d.n	4
		1152.4.d.o	4
		1152.4.d.p	8
		1152.4.d.q	8
1152.4.f	\(\chi_{1152}(575, \cdot)\)	1152.4.f.a	4	1
		1152.4.f.b	4
		1152.4.f.c	4
		1152.4.f.d	4
		1152.4.f.e	8
		1152.4.f.f	12
		1152.4.f.g	12
1152.4.i	\(\chi_{1152}(385, \cdot)\)	n/a	288	2
1152.4.k	\(\chi_{1152}(289, \cdot)\)	n/a	116	2
1152.4.l	\(\chi_{1152}(287, \cdot)\)	1152.4.l.a	48	2
		1152.4.l.b	48
1152.4.p	\(\chi_{1152}(191, \cdot)\)	n/a	288	2
1152.4.r	\(\chi_{1152}(193, \cdot)\)	n/a	288	2
1152.4.s	\(\chi_{1152}(383, \cdot)\)	n/a	288	2
1152.4.v	\(\chi_{1152}(145, \cdot)\)	n/a	236	4
1152.4.w	\(\chi_{1152}(143, \cdot)\)	n/a	192	4
1152.4.y	\(\chi_{1152}(95, \cdot)\)	n/a	560	4
1152.4.bb	\(\chi_{1152}(97, \cdot)\)	n/a	560	4
1152.4.bd	\(\chi_{1152}(73, \cdot)\)	None	0	8
1152.4.be	\(\chi_{1152}(71, \cdot)\)	None	0	8
1152.4.bg	\(\chi_{1152}(49, \cdot)\)	n/a	1136	8
1152.4.bj	\(\chi_{1152}(47, \cdot)\)	n/a	1136	8
1152.4.bl	\(\chi_{1152}(37, \cdot)\)	n/a	3824	16
1152.4.bm	\(\chi_{1152}(35, \cdot)\)	n/a	3072	16
1152.4.bp	\(\chi_{1152}(23, \cdot)\)	None	0	16
1152.4.bq	\(\chi_{1152}(25, \cdot)\)	None	0	16
1152.4.bs	\(\chi_{1152}(11, \cdot)\)	n/a	18368	32
1152.4.bv	\(\chi_{1152}(13, \cdot)\)	n/a	18368	32

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1152))\) into lower level spaces

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