Space of modular forms of level 1152 and weight 2

• Label: 1152.2
• Level: 1152
• Weight: 2
• Dimension: 16200
• Nonzero newspaces: 20
• Sturm bound: 147456
• Trace bound: 33

Defining parameters

Level:	\( N \)	=	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(147456\)
Trace bound:			\(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1152))\).

	Total	New	Old
Modular forms	38144	16632	21512
Cusp forms	35585	16200	19385
Eisenstein series	2559	432	2127

Trace form

16200 * 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 - 44 * q^23 - 64 * q^24 - 76 * q^25 - 48 * q^26 - 48 * q^27 - 144 * q^28 - 64 * q^29 - 64 * q^30 - 56 * q^31 - 48 * q^32 - 128 * q^33 - 48 * q^34 - 60 * q^35 - 64 * q^36 - 160 * q^37 - 48 * q^38 - 48 * q^39 - 48 * q^40 - 76 * q^41 - 64 * q^42 - 44 * q^43 - 48 * q^44 - 64 * q^45 - 144 * q^46 - 24 * q^47 - 64 * q^48 - 44 * q^49 - 48 * q^51 + 48 * q^52 - 16 * q^53 - 64 * q^54 - 76 * q^55 + 64 * q^56 - 80 * q^57 + 96 * q^58 - 4 * q^59 - 64 * q^60 + 16 * q^61 + 48 * q^62 - 48 * q^63 + 48 * q^64 + 16 * q^65 - 64 * q^66 + 4 * q^67 + 48 * q^68 - 40 * q^69 + 144 * q^70 - 4 * q^71 - 64 * q^72 - 116 * q^73 + 64 * q^74 - 8 * q^75 + 80 * q^76 + 68 * q^77 - 64 * q^78 + 24 * q^79 - 32 * q^81 - 144 * q^82 + 84 * q^83 - 64 * q^84 + 88 * q^85 - 48 * q^86 + 64 * q^87 - 48 * q^88 + 132 * q^89 - 64 * q^90 + 36 * q^91 - 48 * q^92 + 32 * q^93 - 48 * q^94 + 144 * q^95 - 64 * q^96 + 96 * q^97 - 48 * q^98 + 80 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1152))\)

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
1152.2.a	\(\chi_{1152}(1, \cdot)\)	1152.2.a.a	1	1
		1152.2.a.b	1
		1152.2.a.c	1
		1152.2.a.d	1
		1152.2.a.e	1
		1152.2.a.f	1
		1152.2.a.g	1
		1152.2.a.h	1
		1152.2.a.i	1
		1152.2.a.j	1
		1152.2.a.k	1
		1152.2.a.l	1
		1152.2.a.m	1
		1152.2.a.n	1
		1152.2.a.o	1
		1152.2.a.p	1
		1152.2.a.q	1
		1152.2.a.r	1
		1152.2.a.s	1
		1152.2.a.t	1
1152.2.c	\(\chi_{1152}(1151, \cdot)\)	1152.2.c.a	4	1
		1152.2.c.b	4
		1152.2.c.c	4
		1152.2.c.d	4
1152.2.d	\(\chi_{1152}(577, \cdot)\)	1152.2.d.a	2	1
		1152.2.d.b	2
		1152.2.d.c	2
		1152.2.d.d	2
		1152.2.d.e	2
		1152.2.d.f	2
		1152.2.d.g	4
		1152.2.d.h	4
1152.2.f	\(\chi_{1152}(575, \cdot)\)	1152.2.f.a	4	1
		1152.2.f.b	4
		1152.2.f.c	4
		1152.2.f.d	4
1152.2.i	\(\chi_{1152}(385, \cdot)\)	1152.2.i.a	2	2
		1152.2.i.b	2
		1152.2.i.c	2
		1152.2.i.d	2
		1152.2.i.e	10
		1152.2.i.f	10
		1152.2.i.g	10
		1152.2.i.h	10
		1152.2.i.i	12
		1152.2.i.j	12
		1152.2.i.k	12
		1152.2.i.l	12
1152.2.k	\(\chi_{1152}(289, \cdot)\)	1152.2.k.a	2	2
		1152.2.k.b	2
		1152.2.k.c	8
		1152.2.k.d	8
		1152.2.k.e	8
		1152.2.k.f	8
1152.2.l	\(\chi_{1152}(287, \cdot)\)	1152.2.l.a	16	2
		1152.2.l.b	16
1152.2.p	\(\chi_{1152}(191, \cdot)\)	1152.2.p.a	4	2
		1152.2.p.b	4
		1152.2.p.c	8
		1152.2.p.d	16
		1152.2.p.e	16
		1152.2.p.f	24
		1152.2.p.g	24
1152.2.r	\(\chi_{1152}(193, \cdot)\)	1152.2.r.a	4	2
		1152.2.r.b	4
		1152.2.r.c	4
		1152.2.r.d	4
		1152.2.r.e	16
		1152.2.r.f	16
		1152.2.r.g	24
		1152.2.r.h	24
1152.2.s	\(\chi_{1152}(383, \cdot)\)	1152.2.s.a	24	2
		1152.2.s.b	24
		1152.2.s.c	24
		1152.2.s.d	24
1152.2.v	\(\chi_{1152}(145, \cdot)\)	1152.2.v.a	4	4
		1152.2.v.b	8
		1152.2.v.c	32
		1152.2.v.d	32
1152.2.w	\(\chi_{1152}(143, \cdot)\)	1152.2.w.a	32	4
		1152.2.w.b	32
1152.2.y	\(\chi_{1152}(95, \cdot)\)	n/a	176	4
1152.2.bb	\(\chi_{1152}(97, \cdot)\)	n/a	176	4
1152.2.bd	\(\chi_{1152}(73, \cdot)\)	None	0	8
1152.2.be	\(\chi_{1152}(71, \cdot)\)	None	0	8
1152.2.bg	\(\chi_{1152}(49, \cdot)\)	n/a	368	8
1152.2.bj	\(\chi_{1152}(47, \cdot)\)	n/a	368	8
1152.2.bl	\(\chi_{1152}(37, \cdot)\)	n/a	1264	16
1152.2.bm	\(\chi_{1152}(35, \cdot)\)	n/a	1024	16
1152.2.bp	\(\chi_{1152}(23, \cdot)\)	None	0	16
1152.2.bq	\(\chi_{1152}(25, \cdot)\)	None	0	16
1152.2.bs	\(\chi_{1152}(11, \cdot)\)	n/a	6080	32
1152.2.bv	\(\chi_{1152}(13, \cdot)\)	n/a	6080	32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1152))\) into lower level spaces

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