Space of modular forms of level 440 and weight 2

• Label: 440.2
• Level: 440
• Weight: 2
• Dimension: 2812
• Nonzero newspaces: 18
• Newform subspaces: 50
• Sturm bound: 23040
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 50 \)
Sturm bound:			\(23040\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(440))\).

	Total	New	Old
Modular forms	6240	3028	3212
Cusp forms	5281	2812	2469
Eisenstein series	959	216	743

Trace form

2812 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 + 2 * q^5 - 44 * q^6 - 4 * q^7 - 12 * q^8 - 14 * q^9 - 22 * q^10 - 48 * q^11 - 56 * q^12 + 4 * q^13 - 36 * q^14 - 28 * q^15 - 76 * q^16 - 8 * q^17 - 68 * q^18 - 14 * q^19 - 62 * q^20 + 24 * q^21 - 36 * q^22 - 20 * q^23 - 68 * q^24 - 14 * q^25 - 76 * q^26 - 6 * q^27 - 4 * q^28 + 32 * q^29 - 60 * q^30 - 40 * q^31 + 8 * q^32 - 62 * q^33 - 48 * q^34 - 76 * q^35 - 140 * q^36 - 12 * q^37 - 72 * q^38 - 156 * q^39 - 12 * q^40 - 144 * q^41 - 192 * q^42 - 140 * q^43 - 144 * q^44 - 28 * q^45 - 136 * q^46 - 128 * q^47 - 224 * q^48 - 114 * q^49 - 132 * q^50 - 186 * q^51 - 160 * q^52 + 28 * q^53 - 228 * q^54 - 68 * q^55 - 296 * q^56 - 22 * q^57 - 128 * q^58 + 10 * q^59 - 160 * q^60 + 84 * q^61 - 132 * q^62 + 16 * q^63 - 84 * q^64 - 48 * q^65 - 76 * q^66 + 80 * q^67 - 60 * q^68 + 64 * q^69 + 40 * q^70 + 28 * q^71 + 104 * q^72 - 112 * q^73 + 120 * q^74 + 52 * q^75 + 100 * q^76 + 36 * q^77 + 328 * q^78 - 20 * q^79 + 128 * q^80 - 176 * q^81 + 252 * q^82 - 90 * q^83 + 284 * q^84 - 64 * q^85 + 44 * q^86 - 144 * q^87 + 300 * q^88 - 168 * q^89 + 118 * q^90 - 288 * q^91 + 172 * q^92 - 180 * q^93 + 156 * q^94 - 166 * q^95 - 16 * q^96 - 162 * q^97 + 176 * q^98 - 316 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)

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
440.2.a	\(\chi_{440}(1, \cdot)\)	440.2.a.a	1	1
		440.2.a.b	1
		440.2.a.c	1
		440.2.a.d	1
		440.2.a.e	2
		440.2.a.f	2
		440.2.a.g	2
440.2.b	\(\chi_{440}(89, \cdot)\)	440.2.b.a	2	1
		440.2.b.b	2
		440.2.b.c	2
		440.2.b.d	8
440.2.c	\(\chi_{440}(219, \cdot)\)	440.2.c.a	4	1
		440.2.c.b	8
		440.2.c.c	56
440.2.f	\(\chi_{440}(351, \cdot)\)	None	0	1
440.2.g	\(\chi_{440}(221, \cdot)\)	440.2.g.a	4	1
		440.2.g.b	12
		440.2.g.c	24
440.2.l	\(\chi_{440}(309, \cdot)\)	440.2.l.a	2	1
		440.2.l.b	2
		440.2.l.c	56
440.2.m	\(\chi_{440}(439, \cdot)\)	None	0	1
440.2.p	\(\chi_{440}(131, \cdot)\)	440.2.p.a	48	1
440.2.r	\(\chi_{440}(67, \cdot)\)	440.2.r.a	2	2
		440.2.r.b	2
		440.2.r.c	2
		440.2.r.d	2
		440.2.r.e	4
		440.2.r.f	4
		440.2.r.g	48
		440.2.r.h	56
440.2.t	\(\chi_{440}(197, \cdot)\)	440.2.t.a	4	2
		440.2.t.b	4
		440.2.t.c	128
440.2.v	\(\chi_{440}(153, \cdot)\)	440.2.v.a	4	2
		440.2.v.b	32
440.2.x	\(\chi_{440}(23, \cdot)\)	None	0	2
440.2.y	\(\chi_{440}(81, \cdot)\)	440.2.y.a	8	4
		440.2.y.b	12
		440.2.y.c	12
		440.2.y.d	16
440.2.z	\(\chi_{440}(51, \cdot)\)	440.2.z.a	192	4
440.2.bc	\(\chi_{440}(39, \cdot)\)	None	0	4
440.2.bd	\(\chi_{440}(69, \cdot)\)	440.2.bd.a	272	4
440.2.bi	\(\chi_{440}(141, \cdot)\)	440.2.bi.a	8	4
		440.2.bi.b	8
		440.2.bi.c	176
440.2.bj	\(\chi_{440}(151, \cdot)\)	None	0	4
440.2.bm	\(\chi_{440}(19, \cdot)\)	440.2.bm.a	8	4
		440.2.bm.b	8
		440.2.bm.c	256
440.2.bn	\(\chi_{440}(9, \cdot)\)	440.2.bn.a	72	4
440.2.bo	\(\chi_{440}(17, \cdot)\)	440.2.bo.a	144	8
440.2.bq	\(\chi_{440}(47, \cdot)\)	None	0	8
440.2.bs	\(\chi_{440}(3, \cdot)\)	440.2.bs.a	544	8
440.2.bu	\(\chi_{440}(13, \cdot)\)	440.2.bu.a	544	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(440))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(440)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 2}\)