Space of modular forms of level 224 and weight 2

• Label: 224.2
• Level: 224
• Weight: 2
• Dimension: 778
• Nonzero newspaces: 12
• Newform subspaces: 23
• Sturm bound: 6144
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 23 \)
Sturm bound:			\(6144\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(224))\).

	Total	New	Old
Modular forms	1728	878	850
Cusp forms	1345	778	567
Eisenstein series	383	100	283

Trace form

778 * q - 16 * q^2 - 10 * q^3 - 16 * q^4 - 12 * q^5 - 16 * q^6 - 14 * q^7 - 40 * q^8 - 22 * q^9 - 32 * q^10 - 10 * q^11 - 48 * q^12 - 28 * q^13 - 36 * q^14 - 36 * q^15 - 56 * q^16 - 16 * q^17 - 56 * q^18 - 10 * q^19 - 48 * q^20 - 20 * q^21 - 64 * q^22 - 26 * q^23 + 8 * q^24 - 26 * q^25 + 24 * q^26 - 64 * q^27 - 20 * q^29 + 48 * q^30 - 50 * q^31 + 24 * q^32 - 44 * q^33 + 8 * q^34 - 38 * q^35 + 16 * q^36 - 12 * q^37 - 32 * q^38 - 76 * q^39 - 40 * q^40 - 48 * q^41 - 40 * q^42 - 56 * q^43 - 96 * q^44 - 100 * q^45 - 80 * q^46 - 54 * q^47 - 120 * q^48 - 46 * q^49 - 120 * q^50 - 62 * q^51 - 32 * q^52 - 124 * q^53 - 40 * q^54 + 12 * q^55 - 32 * q^56 - 160 * q^57 - 8 * q^58 + 6 * q^59 - 8 * q^60 - 108 * q^61 + 24 * q^62 - 30 * q^63 + 32 * q^64 - 68 * q^65 + 32 * q^66 + 34 * q^67 - 56 * q^68 - 128 * q^69 - 8 * q^70 + 24 * q^71 - 64 * q^72 - 16 * q^73 - 48 * q^74 - 16 * q^75 - 16 * q^76 - 36 * q^77 - 120 * q^78 - 18 * q^79 - 8 * q^80 + 6 * q^81 - 16 * q^82 - 96 * q^83 - 40 * q^84 - 72 * q^85 + 24 * q^86 - 140 * q^87 - 24 * q^88 - 48 * q^89 + 104 * q^90 - 20 * q^91 + 56 * q^92 + 56 * q^93 + 104 * q^94 - 94 * q^95 + 216 * q^96 + 16 * q^97 + 168 * q^98 - 72 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)

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
224.2.a	\(\chi_{224}(1, \cdot)\)	224.2.a.a	1	1
		224.2.a.b	1
		224.2.a.c	2
		224.2.a.d	2
224.2.b	\(\chi_{224}(113, \cdot)\)	224.2.b.a	2	1
		224.2.b.b	4
224.2.e	\(\chi_{224}(111, \cdot)\)	224.2.e.a	2	1
		224.2.e.b	4
224.2.f	\(\chi_{224}(223, \cdot)\)	224.2.f.a	8	1
224.2.i	\(\chi_{224}(65, \cdot)\)	224.2.i.a	4	2
		224.2.i.b	4
		224.2.i.c	4
		224.2.i.d	4
224.2.j	\(\chi_{224}(55, \cdot)\)	None	0	2
224.2.m	\(\chi_{224}(57, \cdot)\)	None	0	2
224.2.p	\(\chi_{224}(31, \cdot)\)	224.2.p.a	16	2
224.2.q	\(\chi_{224}(47, \cdot)\)	224.2.q.a	12	2
224.2.t	\(\chi_{224}(81, \cdot)\)	224.2.t.a	12	2
224.2.u	\(\chi_{224}(29, \cdot)\)	224.2.u.a	4	4
		224.2.u.b	40
		224.2.u.c	52
224.2.x	\(\chi_{224}(27, \cdot)\)	224.2.x.a	8	4
		224.2.x.b	112
224.2.z	\(\chi_{224}(87, \cdot)\)	None	0	4
224.2.ba	\(\chi_{224}(9, \cdot)\)	None	0	4
224.2.bd	\(\chi_{224}(37, \cdot)\)	224.2.bd.a	240	8
224.2.be	\(\chi_{224}(3, \cdot)\)	224.2.be.a	240	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(224))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(224)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)