Space of modular forms of level 112 and weight 4

• Label: 112.4
• Level: 112
• Weight: 4
• Dimension: 599
• Nonzero newspaces: 8
• Newform subspaces: 29
• Sturm bound: 3072
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 29 \)
Sturm bound:			\(3072\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(112))\).

	Total	New	Old
Modular forms	1236	643	593
Cusp forms	1068	599	469
Eisenstein series	168	44	124

Trace form

599 * q - 8 * q^2 - 13 * q^3 - 28 * q^4 - 7 * q^5 + 52 * q^6 + 15 * q^7 + 64 * q^8 + 19 * q^9 + 124 * q^10 - 133 * q^11 - 212 * q^12 - 58 * q^13 - 200 * q^14 + 246 * q^15 - 572 * q^16 - 119 * q^17 - 360 * q^18 - 139 * q^19 + 380 * q^20 - 151 * q^21 + 1152 * q^22 + 5 * q^23 + 1684 * q^24 + 743 * q^25 + 516 * q^26 + 578 * q^27 - 292 * q^28 + 278 * q^29 - 2484 * q^30 - 705 * q^31 - 1948 * q^32 - 443 * q^33 - 884 * q^34 - 1055 * q^35 + 1168 * q^36 - 427 * q^37 + 2452 * q^38 - 734 * q^39 + 2660 * q^40 + 390 * q^41 + 3260 * q^42 + 2368 * q^43 + 1948 * q^44 + 2112 * q^45 - 176 * q^46 + 3241 * q^47 - 3428 * q^48 - 4065 * q^49 - 3576 * q^50 + 1541 * q^51 - 4184 * q^52 - 1127 * q^53 - 6164 * q^54 - 1138 * q^55 - 4144 * q^56 - 4742 * q^57 - 4144 * q^58 - 5789 * q^59 - 5508 * q^60 - 4135 * q^61 - 1256 * q^62 - 2871 * q^63 + 380 * q^64 + 2350 * q^65 + 7444 * q^66 - 3265 * q^67 + 7808 * q^68 + 1422 * q^69 + 7268 * q^70 - 80 * q^71 + 3948 * q^72 - 959 * q^73 + 892 * q^74 + 7836 * q^75 + 2444 * q^76 + 3277 * q^77 + 1520 * q^78 + 10157 * q^79 + 5284 * q^80 + 3246 * q^81 + 1396 * q^82 + 10072 * q^83 - 1972 * q^84 + 4082 * q^85 - 7540 * q^86 + 2322 * q^87 - 3068 * q^88 + 1113 * q^89 - 6396 * q^90 + 3466 * q^91 - 4516 * q^92 + 5525 * q^93 - 7556 * q^94 - 2141 * q^95 - 6628 * q^96 - 1442 * q^97 - 5604 * q^98 - 7868 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(112))\)

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
112.4.a	\(\chi_{112}(1, \cdot)\)	112.4.a.a	1	1
		112.4.a.b	1
		112.4.a.c	1
		112.4.a.d	1
		112.4.a.e	1
		112.4.a.f	1
		112.4.a.g	1
		112.4.a.h	2
112.4.b	\(\chi_{112}(57, \cdot)\)	None	0	1
112.4.e	\(\chi_{112}(55, \cdot)\)	None	0	1
112.4.f	\(\chi_{112}(111, \cdot)\)	112.4.f.a	4	1
		112.4.f.b	8
112.4.i	\(\chi_{112}(65, \cdot)\)	112.4.i.a	2	2
		112.4.i.b	2
		112.4.i.c	2
		112.4.i.d	4
		112.4.i.e	6
		112.4.i.f	6
112.4.j	\(\chi_{112}(27, \cdot)\)	112.4.j.a	4	2
		112.4.j.b	88
112.4.m	\(\chi_{112}(29, \cdot)\)	112.4.m.a	34	2
		112.4.m.b	38
112.4.p	\(\chi_{112}(31, \cdot)\)	112.4.p.a	2	2
		112.4.p.b	2
		112.4.p.c	2
		112.4.p.d	2
		112.4.p.e	4
		112.4.p.f	6
		112.4.p.g	6
112.4.q	\(\chi_{112}(87, \cdot)\)	None	0	2
112.4.t	\(\chi_{112}(9, \cdot)\)	None	0	2
112.4.v	\(\chi_{112}(3, \cdot)\)	112.4.v.a	184	4
112.4.w	\(\chi_{112}(37, \cdot)\)	112.4.w.a	184	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces

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