Space of modular forms of level 2592 and weight 2

• Label: 2592.2
• Level: 2592
• Weight: 2
• Dimension: 82384
• Nonzero newspaces: 24
• Sturm bound: 746496
• Trace bound: 89

Defining parameters

Level:	\( N \)	=	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(746496\)
Trace bound:			\(89\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2592))\).

	Total	New	Old
Modular forms	190080	83504	106576
Cusp forms	183169	82384	100785
Eisenstein series	6911	1120	5791

Trace form

82384 * q - 96 * q^2 - 108 * q^3 - 160 * q^4 - 96 * q^5 - 144 * q^6 - 120 * q^7 - 96 * q^8 - 216 * q^9 - 232 * q^10 - 72 * q^11 - 144 * q^12 - 160 * q^13 - 96 * q^14 - 108 * q^15 - 160 * q^16 - 48 * q^17 - 144 * q^18 - 174 * q^19 - 96 * q^20 - 144 * q^21 - 160 * q^22 - 72 * q^23 - 144 * q^24 - 240 * q^25 - 96 * q^26 - 108 * q^27 - 232 * q^28 - 96 * q^29 - 144 * q^30 - 120 * q^31 - 96 * q^32 - 360 * q^33 - 160 * q^34 - 78 * q^35 - 144 * q^36 - 232 * q^37 - 96 * q^38 - 108 * q^39 - 160 * q^40 - 144 * q^41 - 144 * q^42 - 120 * q^43 - 96 * q^44 - 144 * q^45 - 232 * q^46 - 72 * q^47 - 144 * q^48 - 80 * q^49 - 96 * q^50 - 108 * q^51 - 160 * q^52 - 96 * q^53 - 144 * q^54 - 194 * q^55 - 96 * q^56 - 216 * q^57 - 160 * q^58 - 108 * q^59 - 144 * q^60 - 208 * q^61 - 96 * q^62 - 108 * q^63 - 232 * q^64 - 336 * q^65 - 144 * q^66 - 168 * q^67 - 96 * q^68 - 144 * q^69 - 160 * q^70 - 150 * q^71 - 144 * q^72 - 396 * q^73 - 96 * q^74 - 108 * q^75 - 160 * q^76 - 192 * q^77 - 144 * q^78 - 168 * q^79 - 96 * q^80 - 72 * q^81 - 448 * q^82 - 132 * q^83 - 144 * q^84 - 208 * q^85 - 96 * q^86 - 108 * q^87 - 160 * q^88 - 168 * q^89 - 144 * q^90 - 202 * q^91 - 96 * q^92 - 144 * q^93 - 128 * q^94 - 102 * q^95 - 144 * q^96 - 400 * q^97 - 96 * q^98 - 108 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2592))\)

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
2592.2.a	\(\chi_{2592}(1, \cdot)\)	2592.2.a.a	1	1
		2592.2.a.b	1
		2592.2.a.c	1
		2592.2.a.d	1
		2592.2.a.e	1
		2592.2.a.f	1
		2592.2.a.g	1
		2592.2.a.h	1
		2592.2.a.i	2
		2592.2.a.j	2
		2592.2.a.k	2
		2592.2.a.l	2
		2592.2.a.m	2
		2592.2.a.n	2
		2592.2.a.o	2
		2592.2.a.p	2
		2592.2.a.q	2
		2592.2.a.r	2
		2592.2.a.s	2
		2592.2.a.t	2
		2592.2.a.u	4
		2592.2.a.v	4
		2592.2.a.w	4
		2592.2.a.x	4
2592.2.c	\(\chi_{2592}(2591, \cdot)\)	2592.2.c.a	8	1
		2592.2.c.b	16
		2592.2.c.c	24
2592.2.d	\(\chi_{2592}(1297, \cdot)\)	2592.2.d.a	2	1
		2592.2.d.b	2
		2592.2.d.c	2
		2592.2.d.d	2
		2592.2.d.e	4
		2592.2.d.f	4
		2592.2.d.g	4
		2592.2.d.h	4
		2592.2.d.i	4
		2592.2.d.j	8
		2592.2.d.k	8
2592.2.f	\(\chi_{2592}(1295, \cdot)\)	2592.2.f.a	4	1
		2592.2.f.b	16
		2592.2.f.c	24
2592.2.i	\(\chi_{2592}(865, \cdot)\)	2592.2.i.a	2	2
		2592.2.i.b	2
		2592.2.i.c	2
		2592.2.i.d	2
		2592.2.i.e	2
		2592.2.i.f	2
		2592.2.i.g	2
		2592.2.i.h	2
		2592.2.i.i	2
		2592.2.i.j	2
		2592.2.i.k	2
		2592.2.i.l	2
		2592.2.i.m	2
		2592.2.i.n	2
		2592.2.i.o	2
		2592.2.i.p	2
		2592.2.i.q	2
		2592.2.i.r	2
		2592.2.i.s	2
		2592.2.i.t	2
		2592.2.i.u	2
		2592.2.i.v	2
		2592.2.i.w	2
		2592.2.i.x	2
		2592.2.i.y	4
		2592.2.i.z	4
		2592.2.i.ba	4
		2592.2.i.bb	4
		2592.2.i.bc	4
		2592.2.i.bd	4
		2592.2.i.be	4
		2592.2.i.bf	4
		2592.2.i.bg	8
		2592.2.i.bh	8
2592.2.k	\(\chi_{2592}(649, \cdot)\)	None	0	2
2592.2.l	\(\chi_{2592}(647, \cdot)\)	None	0	2
2592.2.p	\(\chi_{2592}(431, \cdot)\)	2592.2.p.a	4	2
		2592.2.p.b	4
		2592.2.p.c	4
		2592.2.p.d	8
		2592.2.p.e	8
		2592.2.p.f	16
		2592.2.p.g	48
2592.2.r	\(\chi_{2592}(433, \cdot)\)	2592.2.r.a	4	2
		2592.2.r.b	4
		2592.2.r.c	4
		2592.2.r.d	4
		2592.2.r.e	4
		2592.2.r.f	4
		2592.2.r.g	4
		2592.2.r.h	4
		2592.2.r.i	4
		2592.2.r.j	4
		2592.2.r.k	4
		2592.2.r.l	4
		2592.2.r.m	4
		2592.2.r.n	8
		2592.2.r.o	8
		2592.2.r.p	8
		2592.2.r.q	16
2592.2.s	\(\chi_{2592}(863, \cdot)\)	2592.2.s.a	8	2
		2592.2.s.b	8
		2592.2.s.c	8
		2592.2.s.d	8
		2592.2.s.e	8
		2592.2.s.f	8
		2592.2.s.g	8
		2592.2.s.h	8
		2592.2.s.i	16
		2592.2.s.j	16
2592.2.v	\(\chi_{2592}(325, \cdot)\)	n/a	752	4
2592.2.w	\(\chi_{2592}(323, \cdot)\)	n/a	752	4
2592.2.y	\(\chi_{2592}(289, \cdot)\)	n/a	216	6
2592.2.z	\(\chi_{2592}(215, \cdot)\)	None	0	4
2592.2.bc	\(\chi_{2592}(217, \cdot)\)	None	0	4
2592.2.bf	\(\chi_{2592}(145, \cdot)\)	n/a	204	6
2592.2.bh	\(\chi_{2592}(143, \cdot)\)	n/a	204	6
2592.2.bi	\(\chi_{2592}(287, \cdot)\)	n/a	216	6
2592.2.bk	\(\chi_{2592}(109, \cdot)\)	n/a	1520	8
2592.2.bn	\(\chi_{2592}(107, \cdot)\)	n/a	1520	8
2592.2.bo	\(\chi_{2592}(97, \cdot)\)	n/a	1944	18
2592.2.bp	\(\chi_{2592}(73, \cdot)\)	None	0	12
2592.2.bs	\(\chi_{2592}(71, \cdot)\)	None	0	12
2592.2.bv	\(\chi_{2592}(47, \cdot)\)	n/a	1908	18
2592.2.bx	\(\chi_{2592}(49, \cdot)\)	n/a	1908	18
2592.2.by	\(\chi_{2592}(95, \cdot)\)	n/a	1944	18
2592.2.cb	\(\chi_{2592}(35, \cdot)\)	n/a	3408	24
2592.2.cc	\(\chi_{2592}(37, \cdot)\)	n/a	3408	24
2592.2.ce	\(\chi_{2592}(23, \cdot)\)	None	0	36
2592.2.ch	\(\chi_{2592}(25, \cdot)\)	None	0	36
2592.2.ci	\(\chi_{2592}(11, \cdot)\)	n/a	30960	72
2592.2.cl	\(\chi_{2592}(13, \cdot)\)	n/a	30960	72

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2592))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2592)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 25}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(648))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(864))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1296))\)\(^{\oplus 2}\)