Space of modular forms of level 112 and weight 6

• Label: 112.6
• Level: 112
• Weight: 6
• Dimension: 1013
• Nonzero newspaces: 8
• Sturm bound: 4608
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(4608\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(112))\).

	Total	New	Old
Modular forms	2004	1057	947
Cusp forms	1836	1013	823
Eisenstein series	168	44	124

Trace form

1013 * q - 8 * q^2 + 11 * q^3 + 36 * q^4 + 29 * q^5 - 236 * q^6 - 121 * q^7 - 512 * q^8 - 119 * q^9 + 860 * q^10 + 2531 * q^11 - 20 * q^12 - 134 * q^13 + 88 * q^14 - 7866 * q^15 + 1732 * q^16 + 1189 * q^17 + 6264 * q^18 + 7621 * q^19 - 5956 * q^20 + 5297 * q^21 - 8864 * q^22 - 2107 * q^23 - 16748 * q^24 - 12471 * q^25 - 14748 * q^26 - 21166 * q^27 + 7324 * q^28 - 6526 * q^29 + 60876 * q^30 + 26623 * q^31 + 47972 * q^32 + 36277 * q^33 + 3468 * q^34 + 13561 * q^35 - 13808 * q^36 - 1999 * q^37 - 106508 * q^38 - 2582 * q^39 - 150556 * q^40 - 16686 * q^41 + 59900 * q^42 + 12224 * q^43 + 109276 * q^44 - 49140 * q^45 + 34992 * q^46 - 92567 * q^47 + 13852 * q^48 - 305795 * q^49 + 117576 * q^50 - 44419 * q^51 - 34008 * q^52 - 6755 * q^53 + 45484 * q^54 + 112574 * q^55 + 58256 * q^56 + 146074 * q^57 - 55728 * q^58 + 99595 * q^59 + 262524 * q^60 + 127181 * q^61 + 237880 * q^62 - 103839 * q^63 + 156348 * q^64 - 202082 * q^65 - 288620 * q^66 - 15385 * q^67 - 344896 * q^68 - 88962 * q^69 - 14972 * q^70 + 114832 * q^71 - 547284 * q^72 + 32349 * q^73 - 294308 * q^74 + 51636 * q^75 + 174924 * q^76 + 61789 * q^77 + 1263536 * q^78 - 72595 * q^79 + 1108900 * q^80 - 48060 * q^81 + 186420 * q^82 - 557528 * q^83 - 190900 * q^84 - 262790 * q^85 - 940948 * q^86 - 313350 * q^87 - 1180668 * q^88 - 184539 * q^89 - 653628 * q^90 + 722562 * q^91 - 26020 * q^92 + 692669 * q^93 + 139964 * q^94 + 893683 * q^95 + 1789724 * q^96 + 368106 * q^97 + 1446012 * q^98 - 1284092 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(112))\)

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
112.6.a	\(\chi_{112}(1, \cdot)\)	112.6.a.a	1	1
		112.6.a.b	1
		112.6.a.c	1
		112.6.a.d	1
		112.6.a.e	1
		112.6.a.f	1
		112.6.a.g	1
		112.6.a.h	2
		112.6.a.i	2
		112.6.a.j	2
		112.6.a.k	2
112.6.b	\(\chi_{112}(57, \cdot)\)	None	0	1
112.6.e	\(\chi_{112}(55, \cdot)\)	None	0	1
112.6.f	\(\chi_{112}(111, \cdot)\)	112.6.f.a	8	1
		112.6.f.b	12
112.6.i	\(\chi_{112}(65, \cdot)\)	112.6.i.a	2	2
		112.6.i.b	4
		112.6.i.c	4
		112.6.i.d	4
		112.6.i.e	4
		112.6.i.f	10
		112.6.i.g	10
112.6.j	\(\chi_{112}(27, \cdot)\)	n/a	156	2
112.6.m	\(\chi_{112}(29, \cdot)\)	n/a	120	2
112.6.p	\(\chi_{112}(31, \cdot)\)	112.6.p.a	12	2
		112.6.p.b	14
		112.6.p.c	14
112.6.q	\(\chi_{112}(87, \cdot)\)	None	0	2
112.6.t	\(\chi_{112}(9, \cdot)\)	None	0	2
112.6.v	\(\chi_{112}(3, \cdot)\)	n/a	312	4
112.6.w	\(\chi_{112}(37, \cdot)\)	n/a	312	4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces

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