Space of modular forms of level 112 and weight 3

• Label: 112.3
• Level: 112
• Weight: 3
• Dimension: 391
• Nonzero newspaces: 8
• Newform subspaces: 16
• Sturm bound: 2304
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 16 \)
Sturm bound:			\(2304\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(112))\).

	Total	New	Old
Modular forms	852	437	415
Cusp forms	684	391	293
Eisenstein series	168	46	122

Trace form

391 * q - 8 * q^2 - 5 * q^3 + 4 * q^4 + q^5 + 4 * q^6 - 5 * q^7 - 32 * q^8 - 21 * q^9 - 84 * q^10 + 27 * q^11 - 116 * q^12 - 28 * q^13 - 24 * q^14 - 18 * q^15 + 68 * q^16 + 41 * q^17 + 136 * q^18 - 21 * q^19 + 156 * q^20 + 77 * q^21 + 80 * q^22 - 57 * q^23 - 108 * q^24 + 23 * q^25 - 204 * q^26 - 140 * q^27 - 68 * q^28 - 102 * q^29 - 116 * q^30 - 105 * q^31 - 28 * q^32 - 163 * q^33 + 140 * q^34 - 53 * q^35 + 80 * q^36 - 87 * q^37 - 92 * q^38 + 284 * q^39 - 92 * q^40 - 36 * q^41 - 420 * q^42 + 138 * q^43 - 580 * q^44 - 546 * q^45 - 608 * q^46 - 153 * q^47 - 804 * q^48 - 73 * q^49 - 536 * q^50 - 441 * q^51 - 536 * q^52 - 447 * q^53 - 244 * q^54 - 528 * q^55 + 240 * q^56 + 186 * q^57 + 592 * q^58 - 325 * q^59 + 1148 * q^60 + 257 * q^61 + 1032 * q^62 + 231 * q^63 + 604 * q^64 + 624 * q^65 + 916 * q^66 + 755 * q^67 + 544 * q^68 + 1228 * q^69 + 724 * q^70 + 1030 * q^71 + 652 * q^72 + 457 * q^73 + 172 * q^74 + 974 * q^75 + 364 * q^76 + 485 * q^77 + 144 * q^78 + 159 * q^79 - 476 * q^80 - 238 * q^81 - 620 * q^82 - 648 * q^83 - 244 * q^84 - 62 * q^85 - 548 * q^86 - 1086 * q^87 + 4 * q^88 - 135 * q^89 + 740 * q^90 - 1268 * q^91 + 540 * q^92 - 647 * q^93 + 1116 * q^94 - 2097 * q^95 + 1948 * q^96 - 612 * q^97 + 972 * q^98 - 1942 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(112))\)

We only show spaces with odd 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
112.3.c	\(\chi_{112}(97, \cdot)\)	112.3.c.a	1	1
		112.3.c.b	2
		112.3.c.c	4
112.3.d	\(\chi_{112}(15, \cdot)\)	112.3.d.a	2	1
		112.3.d.b	4
112.3.g	\(\chi_{112}(71, \cdot)\)	None	0	1
112.3.h	\(\chi_{112}(41, \cdot)\)	None	0	1
112.3.k	\(\chi_{112}(43, \cdot)\)	112.3.k.a	48	2
112.3.l	\(\chi_{112}(13, \cdot)\)	112.3.l.a	4	2
		112.3.l.b	56
112.3.n	\(\chi_{112}(73, \cdot)\)	None	0	2
112.3.o	\(\chi_{112}(23, \cdot)\)	None	0	2
112.3.r	\(\chi_{112}(79, \cdot)\)	112.3.r.a	4	2
		112.3.r.b	6
		112.3.r.c	6
112.3.s	\(\chi_{112}(17, \cdot)\)	112.3.s.a	2	2
		112.3.s.b	4
		112.3.s.c	8
112.3.u	\(\chi_{112}(11, \cdot)\)	112.3.u.a	120	4
112.3.x	\(\chi_{112}(5, \cdot)\)	112.3.x.a	120	4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces

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