Space of modular forms of level 112 and weight 5

• Label: 112.5
• Level: 112
• Weight: 5
• Dimension: 805
• Nonzero newspaces: 8
• Newform subspaces: 18
• Sturm bound: 3840
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 18 \)
Sturm bound:			\(3840\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(112))\).

	Total	New	Old
Modular forms	1620	851	769
Cusp forms	1452	805	647
Eisenstein series	168	46	122

Trace form

805 * q - 8 * q^2 - 5 * q^3 + 4 * q^4 - 83 * q^5 - 140 * q^6 - 5 * q^7 + 160 * q^8 + 441 * q^9 + 188 * q^10 - 197 * q^11 + 652 * q^12 - 720 * q^13 - 56 * q^14 - 18 * q^15 + 324 * q^16 + 485 * q^17 - 2792 * q^18 + 2651 * q^19 - 3812 * q^20 - 1051 * q^21 - 1824 * q^22 - 4465 * q^23 + 3732 * q^24 - 1007 * q^25 + 6820 * q^26 + 3316 * q^27 + 3772 * q^28 + 5230 * q^29 + 7468 * q^30 + 4407 * q^31 - 6428 * q^32 - 2611 * q^33 - 15028 * q^34 - 485 * q^35 - 22960 * q^36 - 1603 * q^37 - 7148 * q^38 - 10372 * q^39 + 10276 * q^40 - 648 * q^41 + 1500 * q^42 - 7582 * q^43 + 11836 * q^44 + 114 * q^45 + 16560 * q^46 + 4311 * q^47 + 25692 * q^48 + 42693 * q^49 - 8664 * q^50 + 16335 * q^51 - 10136 * q^52 + 8365 * q^53 - 3604 * q^54 + 23536 * q^55 - 2384 * q^56 + 1146 * q^57 + 13936 * q^58 - 4229 * q^59 - 19972 * q^60 - 19731 * q^61 - 33768 * q^62 - 14889 * q^63 - 67172 * q^64 - 21328 * q^65 - 74828 * q^66 - 2133 * q^67 - 10336 * q^68 - 2276 * q^69 + 45892 * q^70 - 28138 * q^71 + 84556 * q^72 + 15701 * q^73 + 47548 * q^74 - 70426 * q^75 + 47980 * q^76 - 17579 * q^77 + 16080 * q^78 - 23865 * q^79 - 2780 * q^80 - 4936 * q^81 - 32044 * q^82 + 34552 * q^83 - 19636 * q^84 + 5082 * q^85 + 9580 * q^86 + 132930 * q^87 - 14588 * q^88 + 7989 * q^89 + 26372 * q^90 + 31660 * q^91 + 69596 * q^92 + 12097 * q^93 + 122748 * q^94 - 65241 * q^95 + 47260 * q^96 + 5704 * q^97 - 22052 * q^98 - 34654 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(112))\)

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
112.5.c	\(\chi_{112}(97, \cdot)\)	112.5.c.a	1	1
		112.5.c.b	2
		112.5.c.c	4
		112.5.c.d	8
112.5.d	\(\chi_{112}(15, \cdot)\)	112.5.d.a	4	1
		112.5.d.b	8
112.5.g	\(\chi_{112}(71, \cdot)\)	None	0	1
112.5.h	\(\chi_{112}(41, \cdot)\)	None	0	1
112.5.k	\(\chi_{112}(43, \cdot)\)	112.5.k.a	96	2
112.5.l	\(\chi_{112}(13, \cdot)\)	112.5.l.a	4	2
		112.5.l.b	120
112.5.n	\(\chi_{112}(73, \cdot)\)	None	0	2
112.5.o	\(\chi_{112}(23, \cdot)\)	None	0	2
112.5.r	\(\chi_{112}(79, \cdot)\)	112.5.r.a	10	2
		112.5.r.b	10
		112.5.r.c	12
112.5.s	\(\chi_{112}(17, \cdot)\)	112.5.s.a	4	2
		112.5.s.b	4
		112.5.s.c	6
		112.5.s.d	16
112.5.u	\(\chi_{112}(11, \cdot)\)	112.5.u.a	248	4
112.5.x	\(\chi_{112}(5, \cdot)\)	112.5.x.a	248	4

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces

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