Space of modular forms of level 504 and weight 2

• Label: 504.2
• Level: 504
• Weight: 2
• Dimension: 2860
• Nonzero newspaces: 30
• Newform subspaces: 81
• Sturm bound: 27648
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 30 \)
Newform subspaces:			\( 81 \)
Sturm bound:			\(27648\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(504))\).

	Total	New	Old
Modular forms	7488	3040	4448
Cusp forms	6337	2860	3477
Eisenstein series	1151	180	971

Trace form

2860 * q - 14 * q^2 - 18 * q^3 - 14 * q^4 - 8 * q^5 - 8 * q^6 - 16 * q^7 - 8 * q^8 - 30 * q^9 - 6 * q^10 + 10 * q^11 + 4 * q^12 - 2 * q^13 - 4 * q^14 + 2 * q^16 - 2 * q^17 - 24 * q^18 - 10 * q^19 - 20 * q^20 + 12 * q^21 - 34 * q^22 + 36 * q^23 - 72 * q^24 - 2 * q^25 - 44 * q^26 - 24 * q^27 - 14 * q^28 - 12 * q^29 - 116 * q^30 + 56 * q^31 - 64 * q^32 - 10 * q^33 + 46 * q^34 + 18 * q^35 - 148 * q^36 + 30 * q^37 - 76 * q^38 - 60 * q^39 - 8 * q^40 + 46 * q^41 - 74 * q^42 - 38 * q^43 - 126 * q^44 + 44 * q^45 - 116 * q^46 - 12 * q^47 - 64 * q^48 + 56 * q^49 - 134 * q^50 - 6 * q^51 - 20 * q^52 + 82 * q^53 - 24 * q^54 + 32 * q^55 - 28 * q^56 - 38 * q^57 - 28 * q^58 + 16 * q^59 + 72 * q^60 + 16 * q^61 + 56 * q^62 - 56 * q^63 - 110 * q^64 + 32 * q^65 + 112 * q^66 + 26 * q^67 + 30 * q^68 - 80 * q^69 - 140 * q^70 - 160 * q^71 + 48 * q^72 - 102 * q^73 - 50 * q^74 - 230 * q^75 - 166 * q^76 - 138 * q^77 - 68 * q^78 - 160 * q^79 - 168 * q^80 - 106 * q^81 - 310 * q^82 - 286 * q^83 - 176 * q^84 - 160 * q^85 - 242 * q^86 - 168 * q^87 - 262 * q^88 - 146 * q^89 - 224 * q^90 - 258 * q^91 - 402 * q^92 - 52 * q^93 - 318 * q^94 - 368 * q^95 - 288 * q^96 - 114 * q^97 - 326 * q^98 - 180 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(504))\)

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
504.2.a	\(\chi_{504}(1, \cdot)\)	504.2.a.a	1	1
		504.2.a.b	1
		504.2.a.c	1
		504.2.a.d	1
		504.2.a.e	1
		504.2.a.f	1
		504.2.a.g	1
		504.2.a.h	1
504.2.b	\(\chi_{504}(55, \cdot)\)	None	0	1
504.2.c	\(\chi_{504}(253, \cdot)\)	504.2.c.a	2	1
		504.2.c.b	4
		504.2.c.c	4
		504.2.c.d	4
		504.2.c.e	8
		504.2.c.f	8
504.2.h	\(\chi_{504}(71, \cdot)\)	None	0	1
504.2.i	\(\chi_{504}(125, \cdot)\)	504.2.i.a	8	1
		504.2.i.b	24
504.2.j	\(\chi_{504}(323, \cdot)\)	504.2.j.a	24	1
504.2.k	\(\chi_{504}(377, \cdot)\)	504.2.k.a	8	1
504.2.p	\(\chi_{504}(307, \cdot)\)	504.2.p.a	2	1
		504.2.p.b	4
		504.2.p.c	4
		504.2.p.d	4
		504.2.p.e	4
		504.2.p.f	4
		504.2.p.g	16
504.2.q	\(\chi_{504}(25, \cdot)\)	504.2.q.a	2	2
		504.2.q.b	2
		504.2.q.c	22
		504.2.q.d	22
504.2.r	\(\chi_{504}(169, \cdot)\)	504.2.r.a	2	2
		504.2.r.b	2
		504.2.r.c	6
		504.2.r.d	8
		504.2.r.e	8
		504.2.r.f	10
504.2.s	\(\chi_{504}(289, \cdot)\)	504.2.s.a	2	2
		504.2.s.b	2
		504.2.s.c	2
		504.2.s.d	2
		504.2.s.e	2
		504.2.s.f	2
		504.2.s.g	2
		504.2.s.h	2
		504.2.s.i	4
504.2.t	\(\chi_{504}(193, \cdot)\)	504.2.t.a	2	2
		504.2.t.b	2
		504.2.t.c	22
		504.2.t.d	22
504.2.w	\(\chi_{504}(205, \cdot)\)	504.2.w.a	184	2
504.2.x	\(\chi_{504}(31, \cdot)\)	None	0	2
504.2.y	\(\chi_{504}(173, \cdot)\)	504.2.y.a	184	2
504.2.z	\(\chi_{504}(95, \cdot)\)	None	0	2
504.2.be	\(\chi_{504}(139, \cdot)\)	504.2.be.a	184	2
504.2.bf	\(\chi_{504}(115, \cdot)\)	504.2.bf.a	4	2
		504.2.bf.b	180
504.2.bk	\(\chi_{504}(19, \cdot)\)	504.2.bk.a	12	2
		504.2.bk.b	32
		504.2.bk.c	32
504.2.bl	\(\chi_{504}(17, \cdot)\)	504.2.bl.a	16	2
504.2.bm	\(\chi_{504}(107, \cdot)\)	504.2.bm.a	8	2
		504.2.bm.b	8
		504.2.bm.c	48
504.2.br	\(\chi_{504}(155, \cdot)\)	504.2.br.a	144	2
504.2.bs	\(\chi_{504}(257, \cdot)\)	504.2.bs.a	48	2
504.2.bt	\(\chi_{504}(11, \cdot)\)	504.2.bt.a	184	2
504.2.bu	\(\chi_{504}(41, \cdot)\)	504.2.bu.a	48	2
504.2.bz	\(\chi_{504}(239, \cdot)\)	None	0	2
504.2.ca	\(\chi_{504}(5, \cdot)\)	504.2.ca.a	184	2
504.2.cb	\(\chi_{504}(23, \cdot)\)	None	0	2
504.2.cc	\(\chi_{504}(293, \cdot)\)	504.2.cc.a	16	2
		504.2.cc.b	168
504.2.ch	\(\chi_{504}(269, \cdot)\)	504.2.ch.a	8	2
		504.2.ch.b	56
504.2.ci	\(\chi_{504}(359, \cdot)\)	None	0	2
504.2.cj	\(\chi_{504}(37, \cdot)\)	504.2.cj.a	8	2
		504.2.cj.b	8
		504.2.cj.c	12
		504.2.cj.d	16
		504.2.cj.e	32
504.2.ck	\(\chi_{504}(199, \cdot)\)	None	0	2
504.2.cp	\(\chi_{504}(223, \cdot)\)	None	0	2
504.2.cq	\(\chi_{504}(277, \cdot)\)	504.2.cq.a	184	2
504.2.cr	\(\chi_{504}(103, \cdot)\)	None	0	2
504.2.cs	\(\chi_{504}(85, \cdot)\)	504.2.cs.a	72	2
		504.2.cs.b	72
504.2.cx	\(\chi_{504}(185, \cdot)\)	504.2.cx.a	48	2
504.2.cy	\(\chi_{504}(347, \cdot)\)	504.2.cy.a	184	2
504.2.cz	\(\chi_{504}(187, \cdot)\)	504.2.cz.a	4	2
		504.2.cz.b	180

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(504))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(504)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 1}\)