Space of modular forms of level 220 and weight 2

• Label: 220.2
• Level: 220
• Weight: 2
• Dimension: 704
• Nonzero newspaces: 12
• Newform subspaces: 26
• Sturm bound: 5760
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 26 \)
Sturm bound:			\(5760\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(220))\).

	Total	New	Old
Modular forms	1640	808	832
Cusp forms	1241	704	537
Eisenstein series	399	104	295

Trace form

704 * q - 6 * q^2 + 4 * q^3 - 10 * q^4 - 20 * q^5 - 30 * q^6 + 6 * q^7 - 18 * q^8 - 2 * q^9 - 32 * q^10 + 10 * q^11 - 20 * q^12 - 10 * q^13 - 20 * q^14 - 4 * q^15 - 54 * q^16 - 30 * q^17 - 48 * q^18 - 22 * q^19 - 32 * q^20 - 112 * q^21 - 70 * q^22 - 22 * q^23 - 70 * q^24 - 54 * q^25 - 88 * q^26 - 8 * q^27 - 60 * q^28 - 22 * q^29 - 20 * q^30 + 8 * q^31 - 36 * q^32 + 20 * q^34 + 19 * q^35 - 4 * q^36 - 56 * q^37 + 40 * q^38 - 2 * q^39 + 28 * q^40 - 70 * q^41 + 80 * q^42 + 60 * q^44 - 180 * q^45 + 20 * q^46 - 38 * q^47 + 100 * q^48 - 124 * q^49 + 48 * q^50 - 114 * q^51 + 8 * q^52 - 194 * q^53 - 90 * q^55 - 120 * q^56 - 186 * q^57 - 96 * q^58 - 124 * q^59 - 60 * q^60 - 182 * q^61 - 160 * q^62 - 104 * q^63 - 130 * q^64 - 110 * q^65 - 160 * q^66 - 94 * q^67 - 116 * q^68 - 106 * q^69 - 40 * q^70 - 16 * q^71 - 86 * q^72 + 30 * q^73 - 100 * q^74 + 34 * q^75 - 40 * q^76 - 50 * q^77 - 26 * q^79 - 32 * q^80 + 88 * q^81 + 18 * q^82 + 38 * q^83 + 80 * q^84 + 59 * q^85 + 70 * q^86 + 124 * q^87 + 150 * q^88 + 62 * q^89 + 198 * q^90 + 102 * q^91 + 80 * q^92 + 144 * q^93 + 180 * q^94 + 97 * q^95 + 240 * q^96 + 64 * q^97 + 172 * q^98 + 180 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)

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
220.2.a	\(\chi_{220}(1, \cdot)\)	220.2.a.a	1	1
		220.2.a.b	1
220.2.b	\(\chi_{220}(89, \cdot)\)	220.2.b.a	2	1
		220.2.b.b	4
220.2.d	\(\chi_{220}(131, \cdot)\)	220.2.d.a	2	1
		220.2.d.b	2
		220.2.d.c	8
		220.2.d.d	12
220.2.g	\(\chi_{220}(219, \cdot)\)	220.2.g.a	8	1
		220.2.g.b	24
220.2.k	\(\chi_{220}(153, \cdot)\)	220.2.k.a	4	2
		220.2.k.b	8
220.2.l	\(\chi_{220}(23, \cdot)\)	220.2.l.a	2	2
		220.2.l.b	2
		220.2.l.c	28
		220.2.l.d	28
220.2.m	\(\chi_{220}(81, \cdot)\)	220.2.m.a	8	4
		220.2.m.b	8
220.2.o	\(\chi_{220}(19, \cdot)\)	220.2.o.a	128	4
220.2.r	\(\chi_{220}(51, \cdot)\)	220.2.r.a	8	4
		220.2.r.b	8
		220.2.r.c	32
		220.2.r.d	48
220.2.t	\(\chi_{220}(9, \cdot)\)	220.2.t.a	24	4
220.2.u	\(\chi_{220}(13, \cdot)\)	220.2.u.a	48	8
220.2.v	\(\chi_{220}(3, \cdot)\)	220.2.v.a	256	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(220))\) into lower level spaces

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