Space of modular forms of level 112 and weight 2

• Label: 112.2
• Level: 112
• Weight: 2
• Dimension: 185
• Nonzero newspaces: 8
• Newform subspaces: 23
• Sturm bound: 1536
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 23 \)
Sturm bound:			\(1536\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(112))\).

	Total	New	Old
Modular forms	468	229	239
Cusp forms	301	185	116
Eisenstein series	167	44	123

Trace form

185 * q - 8 * q^2 - 5 * q^3 - 12 * q^4 - 11 * q^5 - 20 * q^6 - 9 * q^7 - 32 * q^8 - 3 * q^9 - 12 * q^10 - 13 * q^11 - 4 * q^12 - 14 * q^13 - 8 * q^14 - 26 * q^15 + 4 * q^16 - 19 * q^17 - 16 * q^18 - 27 * q^19 - 20 * q^20 - 31 * q^21 - 24 * q^22 - 27 * q^23 - 12 * q^24 - 27 * q^25 - 20 * q^26 - 14 * q^27 - 20 * q^28 - 54 * q^29 - 4 * q^30 - q^31 - 28 * q^32 - 43 * q^33 - 20 * q^34 - 23 * q^35 - 16 * q^36 - 39 * q^37 + 12 * q^38 - 6 * q^39 + 4 * q^40 - 6 * q^41 + 60 * q^42 - 32 * q^43 + 44 * q^44 + 20 * q^45 + 24 * q^46 - 23 * q^47 + 92 * q^48 + q^49 + 72 * q^50 + 13 * q^51 + 104 * q^52 + 53 * q^53 + 156 * q^54 + 30 * q^55 + 80 * q^56 + 90 * q^57 + 96 * q^58 + 27 * q^59 + 156 * q^60 + 69 * q^61 + 64 * q^62 + 17 * q^63 + 60 * q^64 - 2 * q^65 + 100 * q^66 + 23 * q^67 + 48 * q^68 + 30 * q^69 + 28 * q^70 - 48 * q^71 + 76 * q^72 - 27 * q^73 - 12 * q^74 - 60 * q^75 - 36 * q^76 - 67 * q^77 - 16 * q^78 - 51 * q^79 - 28 * q^80 - 104 * q^81 - 12 * q^82 - 56 * q^83 - 4 * q^84 - 86 * q^85 - 12 * q^86 - 54 * q^87 - 28 * q^88 - 51 * q^89 - 76 * q^90 + 50 * q^91 + 12 * q^92 - 83 * q^93 - 52 * q^94 + 51 * q^95 - 100 * q^96 - 46 * q^97 - 76 * q^98 + 100 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)

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
112.2.a	\(\chi_{112}(1, \cdot)\)	112.2.a.a	1	1
		112.2.a.b	1
		112.2.a.c	1
112.2.b	\(\chi_{112}(57, \cdot)\)	None	0	1
112.2.e	\(\chi_{112}(55, \cdot)\)	None	0	1
112.2.f	\(\chi_{112}(111, \cdot)\)	112.2.f.a	2	1
		112.2.f.b	2
112.2.i	\(\chi_{112}(65, \cdot)\)	112.2.i.a	2	2
		112.2.i.b	2
		112.2.i.c	2
112.2.j	\(\chi_{112}(27, \cdot)\)	112.2.j.a	4	2
		112.2.j.b	4
		112.2.j.c	4
		112.2.j.d	16
112.2.m	\(\chi_{112}(29, \cdot)\)	112.2.m.a	2	2
		112.2.m.b	2
		112.2.m.c	8
		112.2.m.d	12
112.2.p	\(\chi_{112}(31, \cdot)\)	112.2.p.a	2	2
		112.2.p.b	2
		112.2.p.c	4
112.2.q	\(\chi_{112}(87, \cdot)\)	None	0	2
112.2.t	\(\chi_{112}(9, \cdot)\)	None	0	2
112.2.v	\(\chi_{112}(3, \cdot)\)	112.2.v.a	56	4
112.2.w	\(\chi_{112}(37, \cdot)\)	112.2.w.a	4	4
		112.2.w.b	4
		112.2.w.c	48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces

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