Space of modular forms of level 222 and weight 2

• Label: 222.2
• Level: 222
• Weight: 2
• Dimension: 343
• Nonzero newspaces: 9
• Newform subspaces: 22
• Sturm bound: 5472
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 222 = 2 \cdot 3 \cdot 37 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 22 \)
Sturm bound:			\(5472\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(222))\).

	Total	New	Old
Modular forms	1512	343	1169
Cusp forms	1225	343	882
Eisenstein series	287	0	287

Trace form

343 * q + q^2 + q^3 + q^4 + 6 * q^5 + q^6 + 8 * q^7 + q^8 + q^9 + 6 * q^10 + 12 * q^11 + q^12 + 14 * q^13 + 8 * q^14 + 6 * q^15 + q^16 + 18 * q^17 + q^18 + 20 * q^19 + 6 * q^20 + 8 * q^21 + 12 * q^22 + 24 * q^23 + q^24 + 31 * q^25 - 4 * q^26 - 11 * q^27 - 16 * q^28 - 42 * q^29 - 66 * q^30 - 184 * q^31 + q^32 - 60 * q^33 - 126 * q^34 - 168 * q^35 - 17 * q^36 - 131 * q^37 - 52 * q^38 - 70 * q^39 - 84 * q^40 - 174 * q^41 - 64 * q^42 - 100 * q^43 + 12 * q^44 + 6 * q^45 - 120 * q^46 - 24 * q^47 - 11 * q^48 - 39 * q^49 + 13 * q^50 + 18 * q^51 + 14 * q^52 + 54 * q^53 + q^54 + 72 * q^55 + 8 * q^56 + 20 * q^57 + 30 * q^58 - 12 * q^59 + 6 * q^60 - 28 * q^61 + 32 * q^62 - 100 * q^63 + q^64 - 78 * q^65 + 12 * q^66 - 4 * q^67 + 18 * q^68 - 120 * q^69 + 48 * q^70 - 72 * q^71 + q^72 - 70 * q^73 + 37 * q^74 - 149 * q^75 + 20 * q^76 - 48 * q^77 + 14 * q^78 - 64 * q^79 + 6 * q^80 - 143 * q^81 + 42 * q^82 + 12 * q^83 + 8 * q^84 - 54 * q^85 + 44 * q^86 - 78 * q^87 + 12 * q^88 + 6 * q^90 + 40 * q^91 + 24 * q^92 + 140 * q^93 + 48 * q^94 + 120 * q^95 + q^96 + 98 * q^97 + 57 * q^98 + 192 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)

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
222.2.a	\(\chi_{222}(1, \cdot)\)	222.2.a.a	1	1
		222.2.a.b	1
		222.2.a.c	1
		222.2.a.d	1
		222.2.a.e	1
222.2.c	\(\chi_{222}(73, \cdot)\)	222.2.c.a	2	1
		222.2.c.b	4
222.2.e	\(\chi_{222}(121, \cdot)\)	222.2.e.a	2	2
		222.2.e.b	2
		222.2.e.c	4
222.2.g	\(\chi_{222}(179, \cdot)\)	222.2.g.a	28	2
222.2.j	\(\chi_{222}(85, \cdot)\)	222.2.j.a	4	2
		222.2.j.b	8
222.2.k	\(\chi_{222}(7, \cdot)\)	222.2.k.a	6	6
		222.2.k.b	6
		222.2.k.c	6
		222.2.k.d	6
		222.2.k.e	12
222.2.m	\(\chi_{222}(23, \cdot)\)	222.2.m.a	56	4
222.2.n	\(\chi_{222}(25, \cdot)\)	222.2.n.a	24	6
		222.2.n.b	24
222.2.q	\(\chi_{222}(5, \cdot)\)	222.2.q.a	144	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(222))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(222)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 2}\)