Space of modular forms of level 468 and weight 2

• Label: 468.2
• Level: 468
• Weight: 2
• Dimension: 2659
• Nonzero newspaces: 30
• Newform subspaces: 81
• Sturm bound: 24192
• Trace bound: 15

Defining parameters

Level:	\( N \)	=	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 30 \)
Newform subspaces:			\( 81 \)
Sturm bound:			\(24192\)
Trace bound:			\(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(468))\).

	Total	New	Old
Modular forms	6528	2859	3669
Cusp forms	5569	2659	2910
Eisenstein series	959	200	759

Trace form

2659 * q - 12 * q^2 - 8 * q^4 - 18 * q^5 - 18 * q^6 + 4 * q^7 - 18 * q^8 - 24 * q^9 - 46 * q^10 - 36 * q^12 - 41 * q^13 - 60 * q^14 - 18 * q^15 - 32 * q^16 - 63 * q^17 - 60 * q^18 + 4 * q^19 - 30 * q^20 - 42 * q^21 + 6 * q^22 + 6 * q^23 - 30 * q^24 + 9 * q^25 + 12 * q^26 + 9 * q^29 + 12 * q^30 + 72 * q^31 + 78 * q^32 - 42 * q^33 + 32 * q^34 + 114 * q^35 + 42 * q^36 - 43 * q^37 + 18 * q^38 + 51 * q^39 - 64 * q^40 + 27 * q^41 + 12 * q^42 + 40 * q^43 - 48 * q^44 - 18 * q^45 - 138 * q^46 + 48 * q^47 - 66 * q^48 + 44 * q^49 - 150 * q^50 + 24 * q^51 - 104 * q^52 - 24 * q^53 - 102 * q^54 - 30 * q^55 - 108 * q^56 - 60 * q^57 - 130 * q^58 - 12 * q^59 - 96 * q^60 - 13 * q^61 - 102 * q^62 - 42 * q^63 - 212 * q^64 - 108 * q^65 - 120 * q^66 - 74 * q^67 - 222 * q^68 - 42 * q^69 - 252 * q^70 - 108 * q^71 - 138 * q^72 - 156 * q^73 - 210 * q^74 - 96 * q^75 - 192 * q^76 - 198 * q^77 - 240 * q^78 - 78 * q^79 - 360 * q^80 - 120 * q^81 - 262 * q^82 - 216 * q^83 - 252 * q^84 - 239 * q^85 - 318 * q^86 - 78 * q^87 - 222 * q^88 - 204 * q^89 - 192 * q^90 - 92 * q^91 - 300 * q^92 - 210 * q^93 - 138 * q^94 - 120 * q^95 - 84 * q^96 - 118 * q^97 - 198 * q^98 - 90 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(468))\)

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
468.2.a	\(\chi_{468}(1, \cdot)\)	468.2.a.a	1	1
		468.2.a.b	1
		468.2.a.c	1
		468.2.a.d	1
		468.2.a.e	1
468.2.b	\(\chi_{468}(181, \cdot)\)	468.2.b.a	2	1
		468.2.b.b	2
		468.2.b.c	2
468.2.c	\(\chi_{468}(287, \cdot)\)	468.2.c.a	4	1
		468.2.c.b	8
		468.2.c.c	12
468.2.h	\(\chi_{468}(467, \cdot)\)	468.2.h.a	4	1
		468.2.h.b	4
		468.2.h.c	4
		468.2.h.d	16
468.2.i	\(\chi_{468}(157, \cdot)\)	468.2.i.a	2	2
		468.2.i.b	10
		468.2.i.c	12
468.2.j	\(\chi_{468}(133, \cdot)\)	468.2.j.a	28	2
468.2.k	\(\chi_{468}(61, \cdot)\)	468.2.k.a	28	2
468.2.l	\(\chi_{468}(217, \cdot)\)	468.2.l.a	2	2
		468.2.l.b	2
		468.2.l.c	2
		468.2.l.d	2
		468.2.l.e	4
468.2.n	\(\chi_{468}(307, \cdot)\)	468.2.n.a	2	2
		468.2.n.b	2
		468.2.n.c	2
		468.2.n.d	2
		468.2.n.e	2
		468.2.n.f	2
		468.2.n.g	2
		468.2.n.h	8
		468.2.n.i	8
		468.2.n.j	10
		468.2.n.k	10
		468.2.n.l	16
468.2.p	\(\chi_{468}(125, \cdot)\)	468.2.p.a	12	2
468.2.s	\(\chi_{468}(35, \cdot)\)	468.2.s.a	4	2
		468.2.s.b	4
		468.2.s.c	8
		468.2.s.d	40
468.2.t	\(\chi_{468}(361, \cdot)\)	468.2.t.a	2	2
		468.2.t.b	2
		468.2.t.c	2
		468.2.t.d	4
468.2.w	\(\chi_{468}(95, \cdot)\)	468.2.w.a	160	2
468.2.x	\(\chi_{468}(155, \cdot)\)	468.2.x.a	160	2
468.2.bc	\(\chi_{468}(23, \cdot)\)	468.2.bc.a	160	2
468.2.bd	\(\chi_{468}(191, \cdot)\)	468.2.bd.a	160	2
468.2.be	\(\chi_{468}(49, \cdot)\)	468.2.be.a	2	2
		468.2.be.b	6
		468.2.be.c	20
468.2.bj	\(\chi_{468}(121, \cdot)\)	468.2.bj.a	2	2
		468.2.bj.b	6
		468.2.bj.c	20
468.2.bk	\(\chi_{468}(131, \cdot)\)	468.2.bk.a	72	2
		468.2.bk.b	72
468.2.bl	\(\chi_{468}(25, \cdot)\)	468.2.bl.a	4	2
		468.2.bl.b	24
468.2.bm	\(\chi_{468}(263, \cdot)\)	468.2.bm.a	160	2
468.2.bp	\(\chi_{468}(179, \cdot)\)	468.2.bp.a	4	2
		468.2.bp.b	4
		468.2.bp.c	8
		468.2.bp.d	40
468.2.bs	\(\chi_{468}(31, \cdot)\)	468.2.bs.a	320	4
468.2.bv	\(\chi_{468}(89, \cdot)\)	468.2.bv.a	16	4
468.2.bw	\(\chi_{468}(149, \cdot)\)	468.2.bw.a	56	4
468.2.bz	\(\chi_{468}(41, \cdot)\)	468.2.bz.a	56	4
468.2.cb	\(\chi_{468}(19, \cdot)\)	468.2.cb.a	4	4
		468.2.cb.b	4
		468.2.cb.c	4
		468.2.cb.d	4
		468.2.cb.e	4
		468.2.cb.f	16
		468.2.cb.g	24
		468.2.cb.h	24
		468.2.cb.i	48
468.2.cc	\(\chi_{468}(115, \cdot)\)	468.2.cc.a	320	4
468.2.cf	\(\chi_{468}(7, \cdot)\)	468.2.cf.a	320	4
468.2.cg	\(\chi_{468}(5, \cdot)\)	468.2.cg.a	56	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(468))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(468)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 2}\)