Space of modular forms of level 112 and weight 10

• Label: 112.10
• Level: 112
• Weight: 10
• Dimension: 1841
• Nonzero newspaces: 8
• Sturm bound: 7680
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(7680\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(112))\).

	Total	New	Old
Modular forms	3540	1885	1655
Cusp forms	3372	1841	1531
Eisenstein series	168	44	124

Trace form

1841 * q - 8 * q^2 + 155 * q^3 - 348 * q^4 + 709 * q^5 + 4372 * q^6 - 1385 * q^7 + 1408 * q^8 - 11627 * q^9 - 9380 * q^10 - 109741 * q^11 - 434324 * q^12 + 86146 * q^13 + 133528 * q^14 - 930906 * q^15 + 1634500 * q^16 - 344227 * q^17 - 4359816 * q^18 + 2559653 * q^19 + 6555964 * q^20 - 2759551 * q^21 + 68576 * q^22 + 1430565 * q^23 - 3727724 * q^24 + 2348589 * q^25 + 12695524 * q^26 - 15473230 * q^27 - 3629540 * q^28 - 1230918 * q^29 + 9355596 * q^30 + 18087423 * q^31 + 3311972 * q^32 - 642155 * q^33 + 9056396 * q^34 - 28934519 * q^35 - 47128304 * q^36 + 28758025 * q^37 + 29992692 * q^38 - 121564070 * q^39 + 23502564 * q^40 - 9595734 * q^41 + 15533180 * q^42 + 198811680 * q^43 - 72280228 * q^44 + 88731780 * q^45 + 317384496 * q^46 - 389588759 * q^47 + 24132892 * q^48 - 1290575879 * q^49 - 545233464 * q^50 + 284022509 * q^51 - 193617368 * q^52 + 294004613 * q^53 + 960636844 * q^54 - 214172066 * q^55 + 655987472 * q^56 + 322857178 * q^57 + 151101648 * q^58 + 43331451 * q^59 - 2719663236 * q^60 - 460728107 * q^61 - 683041736 * q^62 - 117147087 * q^63 + 1749389628 * q^64 + 1052934718 * q^65 + 2452878100 * q^66 - 606325321 * q^67 - 79371456 * q^68 - 1936679202 * q^69 - 2781321212 * q^70 - 654645936 * q^71 - 153538644 * q^72 - 634078251 * q^73 - 247821732 * q^74 + 2265797796 * q^75 + 906538188 * q^76 + 1629494525 * q^77 + 3470049584 * q^78 - 2381356403 * q^79 + 1400545700 * q^80 + 657170160 * q^81 + 1348575156 * q^82 - 805955192 * q^83 - 1281919924 * q^84 - 2814167990 * q^85 - 487961364 * q^86 + 3992098986 * q^87 - 3562294268 * q^88 + 1946820477 * q^89 - 6289106748 * q^90 - 820048046 * q^91 + 357523548 * q^92 - 1352778547 * q^93 + 15599499452 * q^94 - 127481037 * q^95 + 7664652572 * q^96 - 578031614 * q^97 - 6954079108 * q^98 + 6210596644 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(112))\)

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
112.10.a	\(\chi_{112}(1, \cdot)\)	112.10.a.a	1	1
		112.10.a.b	1
		112.10.a.c	2
		112.10.a.d	2
		112.10.a.e	2
		112.10.a.f	2
		112.10.a.g	3
		112.10.a.h	3
		112.10.a.i	3
		112.10.a.j	4
		112.10.a.k	4
112.10.b	\(\chi_{112}(57, \cdot)\)	None	0	1
112.10.e	\(\chi_{112}(55, \cdot)\)	None	0	1
112.10.f	\(\chi_{112}(111, \cdot)\)	112.10.f.a	12	1
		112.10.f.b	24
112.10.i	\(\chi_{112}(65, \cdot)\)	112.10.i.a	6	2
		112.10.i.b	6
		112.10.i.c	10
		112.10.i.d	12
		112.10.i.e	18
		112.10.i.f	18
112.10.j	\(\chi_{112}(27, \cdot)\)	n/a	284	2
112.10.m	\(\chi_{112}(29, \cdot)\)	n/a	216	2
112.10.p	\(\chi_{112}(31, \cdot)\)	112.10.p.a	24	2
		112.10.p.b	24
		112.10.p.c	24
112.10.q	\(\chi_{112}(87, \cdot)\)	None	0	2
112.10.t	\(\chi_{112}(9, \cdot)\)	None	0	2
112.10.v	\(\chi_{112}(3, \cdot)\)	n/a	568	4
112.10.w	\(\chi_{112}(37, \cdot)\)	n/a	568	4

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces

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