Space of modular forms of level 220 and weight 4

• Label: 220.4
• Level: 220
• Weight: 4
• Dimension: 2216
• Nonzero newspaces: 12
• Newform subspaces: 25
• Sturm bound: 11520
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 25 \)
Sturm bound:			\(11520\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(220))\).

	Total	New	Old
Modular forms	4520	2320	2200
Cusp forms	4120	2216	1904
Eisenstein series	400	104	296

Trace form

2216 * q - 6 * q^2 - 8 * q^3 - 10 * q^4 - 60 * q^5 - 46 * q^6 + 52 * q^7 + 78 * q^8 + 38 * q^9 + 128 * q^10 - 80 * q^11 + 140 * q^12 - 316 * q^13 - 360 * q^14 - 454 * q^15 - 758 * q^16 + 552 * q^17 - 172 * q^18 + 698 * q^19 - 172 * q^20 + 872 * q^21 + 890 * q^22 + 864 * q^23 + 890 * q^24 + 236 * q^25 + 940 * q^26 - 26 * q^27 + 700 * q^28 - 972 * q^29 + 1580 * q^30 - 1436 * q^31 + 1244 * q^32 - 3470 * q^33 + 1860 * q^34 - 476 * q^35 - 1044 * q^36 - 1340 * q^37 - 3860 * q^38 - 1292 * q^39 - 4772 * q^40 + 1348 * q^41 - 6920 * q^42 + 1060 * q^43 - 3020 * q^44 + 2120 * q^45 + 164 * q^46 + 224 * q^47 + 2900 * q^48 + 1066 * q^49 + 4378 * q^50 + 1998 * q^51 - 192 * q^52 - 3468 * q^53 + 1470 * q^55 - 2136 * q^56 - 1262 * q^57 - 3044 * q^58 + 3246 * q^59 - 3500 * q^60 + 6912 * q^61 + 3060 * q^62 + 6648 * q^63 + 7550 * q^64 + 5400 * q^65 + 10100 * q^66 + 4332 * q^67 + 12516 * q^68 + 1304 * q^69 + 10480 * q^70 - 1008 * q^71 + 15434 * q^72 - 4016 * q^73 + 3760 * q^74 - 7666 * q^75 - 1640 * q^76 - 11280 * q^77 - 16200 * q^78 - 7516 * q^79 - 11712 * q^80 - 18564 * q^81 - 15062 * q^82 - 1066 * q^83 - 11800 * q^84 - 6806 * q^85 - 1646 * q^86 + 4888 * q^87 - 11530 * q^88 + 7592 * q^89 + 8788 * q^90 + 10736 * q^91 + 7520 * q^92 + 15112 * q^93 + 3760 * q^94 + 5862 * q^95 + 6784 * q^96 + 11610 * q^97 + 4388 * q^98 - 6440 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(220))\)

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
220.4.a	\(\chi_{220}(1, \cdot)\)	220.4.a.a	1	1
		220.4.a.b	1
		220.4.a.c	1
		220.4.a.d	2
		220.4.a.e	2
		220.4.a.f	3
220.4.b	\(\chi_{220}(89, \cdot)\)	220.4.b.a	2	1
		220.4.b.b	6
		220.4.b.c	6
220.4.d	\(\chi_{220}(131, \cdot)\)	220.4.d.a	36	1
		220.4.d.b	36
220.4.g	\(\chi_{220}(219, \cdot)\)	220.4.g.a	8	1
		220.4.g.b	96
220.4.k	\(\chi_{220}(153, \cdot)\)	220.4.k.a	8	2
		220.4.k.b	28
220.4.l	\(\chi_{220}(23, \cdot)\)	220.4.l.a	90	2
		220.4.l.b	90
220.4.m	\(\chi_{220}(81, \cdot)\)	220.4.m.a	24	4
		220.4.m.b	24
220.4.o	\(\chi_{220}(19, \cdot)\)	220.4.o.a	416	4
220.4.r	\(\chi_{220}(51, \cdot)\)	220.4.r.a	144	4
		220.4.r.b	144
220.4.t	\(\chi_{220}(9, \cdot)\)	220.4.t.a	72	4
220.4.u	\(\chi_{220}(13, \cdot)\)	220.4.u.a	144	8
220.4.v	\(\chi_{220}(3, \cdot)\)	220.4.v.a	832	8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(220))\) into lower level spaces

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