Space of modular forms of level 228 and weight 2

• Label: 228.2
• Level: 228
• Weight: 2
• Dimension: 594
• Nonzero newspaces: 12
• Newform subspaces: 24
• Sturm bound: 5760
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 24 \)
Sturm bound:			\(5760\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(228))\).

	Total	New	Old
Modular forms	1620	658	962
Cusp forms	1261	594	667
Eisenstein series	359	64	295

Trace form

594 * q - 18 * q^4 - 9 * q^6 - 18 * q^9 - 18 * q^10 - 9 * q^12 - 12 * q^13 + 18 * q^15 - 18 * q^16 + 18 * q^17 - 18 * q^18 + 42 * q^19 + 3 * q^21 - 18 * q^22 + 18 * q^23 - 9 * q^24 - 6 * q^27 - 72 * q^28 - 36 * q^29 - 72 * q^30 - 36 * q^31 - 90 * q^32 - 72 * q^33 - 108 * q^34 - 72 * q^35 - 99 * q^36 - 108 * q^37 - 126 * q^38 - 54 * q^39 - 144 * q^40 - 36 * q^41 - 99 * q^42 - 72 * q^43 - 90 * q^44 - 99 * q^45 - 108 * q^46 - 36 * q^47 - 72 * q^48 - 72 * q^49 - 54 * q^50 - 54 * q^51 - 18 * q^52 - 9 * q^54 - 63 * q^57 - 36 * q^58 - 18 * q^60 - 120 * q^61 + 90 * q^62 - 42 * q^63 + 126 * q^64 - 108 * q^65 + 63 * q^66 - 72 * q^67 + 126 * q^68 - 189 * q^69 + 198 * q^70 - 36 * q^71 + 45 * q^72 - 198 * q^73 + 144 * q^74 - 42 * q^75 + 162 * q^76 - 234 * q^77 + 63 * q^78 - 48 * q^79 + 144 * q^80 + 18 * q^81 + 252 * q^82 + 18 * q^83 + 99 * q^84 - 252 * q^85 + 126 * q^86 + 36 * q^87 + 126 * q^88 - 54 * q^89 + 54 * q^90 + 24 * q^91 + 90 * q^92 + 12 * q^93 + 54 * q^95 + 54 * q^96 + 18 * q^97 + 135 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)

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
228.2.a	\(\chi_{228}(1, \cdot)\)	228.2.a.a	1	1
		228.2.a.b	1
		228.2.a.c	2
228.2.c	\(\chi_{228}(191, \cdot)\)	228.2.c.a	36	1
228.2.d	\(\chi_{228}(113, \cdot)\)	228.2.d.a	2	1
		228.2.d.b	4
228.2.f	\(\chi_{228}(151, \cdot)\)	228.2.f.a	10	1
		228.2.f.b	10
228.2.i	\(\chi_{228}(49, \cdot)\)	228.2.i.a	4	2
		228.2.i.b	4
228.2.k	\(\chi_{228}(31, \cdot)\)	228.2.k.a	20	2
		228.2.k.b	20
228.2.m	\(\chi_{228}(11, \cdot)\)	228.2.m.a	72	2
228.2.p	\(\chi_{228}(65, \cdot)\)	228.2.p.a	2	2
		228.2.p.b	2
		228.2.p.c	4
		228.2.p.d	4
228.2.q	\(\chi_{228}(25, \cdot)\)	228.2.q.a	6	6
		228.2.q.b	12
228.2.t	\(\chi_{228}(29, \cdot)\)	228.2.t.a	6	6
		228.2.t.b	36
228.2.v	\(\chi_{228}(23, \cdot)\)	228.2.v.a	216	6
228.2.w	\(\chi_{228}(67, \cdot)\)	228.2.w.a	60	6
		228.2.w.b	60

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(228))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(228)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)