Space of modular forms of level 224 and weight 6

• Label: 224.6
• Level: 224
• Weight: 6
• Dimension: 4090
• Nonzero newspaces: 12
• Sturm bound: 18432
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(18432\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(224))\).

	Total	New	Old
Modular forms	7872	4190	3682
Cusp forms	7488	4090	3398
Eisenstein series	384	100	284

Trace form

4090 * q - 16 * q^2 - 10 * q^3 - 16 * q^4 - 92 * q^5 - 16 * q^6 + 82 * q^7 - 40 * q^8 - 598 * q^9 + 384 * q^10 - 10 * q^11 + 3152 * q^12 - 236 * q^13 - 2500 * q^14 - 868 * q^15 - 8376 * q^16 - 3632 * q^17 + 3224 * q^18 - 10 * q^19 + 15184 * q^20 + 5868 * q^21 + 24720 * q^22 + 1318 * q^23 - 42936 * q^24 + 5414 * q^25 - 25976 * q^26 + 14912 * q^27 + 2160 * q^28 - 7396 * q^29 + 64608 * q^30 - 71986 * q^31 + 37144 * q^32 - 21708 * q^33 + 12488 * q^34 + 4762 * q^35 - 131216 * q^36 + 14500 * q^37 - 832 * q^38 + 158548 * q^39 + 57880 * q^40 + 70640 * q^41 + 53600 * q^42 - 112280 * q^43 - 7456 * q^44 - 57588 * q^45 - 126672 * q^46 - 11574 * q^47 - 224760 * q^48 + 160194 * q^49 + 9000 * q^50 + 15266 * q^51 - 36960 * q^52 + 146804 * q^53 - 2648 * q^54 - 194356 * q^55 + 80960 * q^56 + 22208 * q^57 + 169128 * q^58 + 14470 * q^59 + 92152 * q^60 - 333948 * q^61 - 126984 * q^62 + 247170 * q^63 + 98336 * q^64 + 65244 * q^65 + 290000 * q^66 + 256194 * q^67 + 302408 * q^68 + 417344 * q^69 + 56272 * q^70 - 66920 * q^71 - 54208 * q^72 + 160656 * q^73 - 426224 * q^74 - 430256 * q^75 - 512016 * q^76 - 180452 * q^77 - 167064 * q^78 - 495762 * q^79 + 194168 * q^80 - 596522 * q^81 - 870416 * q^82 + 658464 * q^83 - 597496 * q^84 + 237208 * q^85 - 539800 * q^86 + 1178644 * q^87 + 399656 * q^88 + 518640 * q^89 + 1600280 * q^90 - 99284 * q^91 + 2240184 * q^92 + 811768 * q^93 + 2086856 * q^94 - 1617054 * q^95 - 187432 * q^96 - 1404432 * q^97 - 1539928 * q^98 - 1410984 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(224))\)

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
224.6.a	\(\chi_{224}(1, \cdot)\)	224.6.a.a	1	1
		224.6.a.b	1
		224.6.a.c	2
		224.6.a.d	2
		224.6.a.e	3
		224.6.a.f	3
		224.6.a.g	4
		224.6.a.h	4
		224.6.a.i	5
		224.6.a.j	5
224.6.b	\(\chi_{224}(113, \cdot)\)	224.6.b.a	14	1
		224.6.b.b	16
224.6.e	\(\chi_{224}(111, \cdot)\)	224.6.e.a	2	1
		224.6.e.b	36
224.6.f	\(\chi_{224}(223, \cdot)\)	224.6.f.a	40	1
224.6.i	\(\chi_{224}(65, \cdot)\)	224.6.i.a	20	2
		224.6.i.b	20
		224.6.i.c	20
		224.6.i.d	20
224.6.j	\(\chi_{224}(55, \cdot)\)	None	0	2
224.6.m	\(\chi_{224}(57, \cdot)\)	None	0	2
224.6.p	\(\chi_{224}(31, \cdot)\)	224.6.p.a	80	2
224.6.q	\(\chi_{224}(47, \cdot)\)	224.6.q.a	76	2
224.6.t	\(\chi_{224}(81, \cdot)\)	224.6.t.a	76	2
224.6.u	\(\chi_{224}(29, \cdot)\)	n/a	480	4
224.6.x	\(\chi_{224}(27, \cdot)\)	n/a	632	4
224.6.z	\(\chi_{224}(87, \cdot)\)	None	0	4
224.6.ba	\(\chi_{224}(9, \cdot)\)	None	0	4
224.6.bd	\(\chi_{224}(37, \cdot)\)	n/a	1264	8
224.6.be	\(\chi_{224}(3, \cdot)\)	n/a	1264	8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(224))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(224)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)