Space of modular forms of level 220 and weight 3

• Label: 220.3
• Level: 220
• Weight: 3
• Dimension: 1460
• Nonzero newspaces: 12
• Newform subspaces: 15
• Sturm bound: 8640
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 15 \)
Sturm bound:			\(8640\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(220))\).

	Total	New	Old
Modular forms	3080	1572	1508
Cusp forms	2680	1460	1220
Eisenstein series	400	112	288

Trace form

1460 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 10 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^8 - 24 * q^9 - 22 * q^10 - 10 * q^11 - 100 * q^12 + 6 * q^13 - 52 * q^14 + 106 * q^15 + 74 * q^16 + 174 * q^17 + 96 * q^18 + 60 * q^19 + 98 * q^20 + 10 * q^22 - 38 * q^23 + 98 * q^24 - 264 * q^25 - 64 * q^26 - 394 * q^27 - 280 * q^28 - 334 * q^29 - 320 * q^30 - 164 * q^31 - 476 * q^32 + 230 * q^33 - 692 * q^34 - 41 * q^35 - 864 * q^36 + 396 * q^37 - 420 * q^38 + 370 * q^39 - 72 * q^40 + 434 * q^41 + 160 * q^42 + 500 * q^43 + 140 * q^44 + 710 * q^45 + 412 * q^46 + 286 * q^47 + 540 * q^48 + 206 * q^49 + 58 * q^50 - 68 * q^51 + 848 * q^52 + 70 * q^53 + 1516 * q^54 + 80 * q^55 + 1072 * q^56 + 112 * q^57 + 772 * q^58 + 270 * q^59 + 380 * q^60 - 610 * q^61 + 600 * q^62 - 876 * q^63 + 238 * q^64 - 1180 * q^65 - 240 * q^66 - 702 * q^67 - 128 * q^68 - 2114 * q^69 - 400 * q^70 - 1072 * q^71 - 1666 * q^72 - 1434 * q^73 - 1512 * q^74 - 16 * q^75 - 1780 * q^76 - 1250 * q^77 - 2240 * q^78 - 470 * q^79 - 712 * q^80 - 88 * q^81 - 1422 * q^82 - 168 * q^83 - 1084 * q^84 + 389 * q^85 - 598 * q^86 + 32 * q^87 - 10 * q^88 + 866 * q^89 - 742 * q^90 + 174 * q^91 - 380 * q^92 + 376 * q^93 - 12 * q^94 - 993 * q^95 - 528 * q^96 - 94 * q^97 - 204 * q^98 - 920 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(220))\)

We only show spaces with odd 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
220.3.c	\(\chi_{220}(111, \cdot)\)	220.3.c.a	40	1
220.3.e	\(\chi_{220}(109, \cdot)\)	220.3.e.a	4	1
		220.3.e.b	8
220.3.f	\(\chi_{220}(21, \cdot)\)	220.3.f.a	8	1
220.3.h	\(\chi_{220}(199, \cdot)\)	220.3.h.a	60	1
220.3.i	\(\chi_{220}(43, \cdot)\)	220.3.i.a	136	2
220.3.j	\(\chi_{220}(133, \cdot)\)	220.3.j.a	20	2
220.3.n	\(\chi_{220}(59, \cdot)\)	220.3.n.a	272	4
220.3.p	\(\chi_{220}(41, \cdot)\)	220.3.p.a	16	4
		220.3.p.b	16
220.3.q	\(\chi_{220}(29, \cdot)\)	220.3.q.a	48	4
220.3.s	\(\chi_{220}(31, \cdot)\)	220.3.s.a	96	4
		220.3.s.b	96
220.3.w	\(\chi_{220}(7, \cdot)\)	220.3.w.a	544	8
220.3.x	\(\chi_{220}(37, \cdot)\)	220.3.x.a	96	8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(220))\) into lower level spaces

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