Space of modular forms of level 224 and weight 3

• Label: 224.3
• Level: 224
• Weight: 3
• Dimension: 1606
• Nonzero newspaces: 12
• Newform subspaces: 26
• Sturm bound: 9216
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 26 \)
Sturm bound:			\(9216\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(224))\).

	Total	New	Old
Modular forms	3264	1706	1558
Cusp forms	2880	1606	1274
Eisenstein series	384	100	284

Trace form

1606 * q - 16 * q^2 - 14 * q^3 - 16 * q^4 - 24 * q^5 - 16 * q^6 - 14 * q^7 - 40 * q^8 + 10 * q^9 + 64 * q^10 + 18 * q^11 + 80 * q^12 + 40 * q^13 - 4 * q^14 - 20 * q^15 - 56 * q^16 - 88 * q^17 - 136 * q^18 - 78 * q^19 - 176 * q^20 - 84 * q^21 - 336 * q^22 + 118 * q^23 - 440 * q^24 + 6 * q^25 - 216 * q^26 + 244 * q^27 - 80 * q^28 + 16 * q^29 - 64 * q^30 - 18 * q^31 + 24 * q^32 - 52 * q^33 + 72 * q^34 - 110 * q^35 + 624 * q^36 + 104 * q^37 + 768 * q^38 - 340 * q^39 + 792 * q^40 + 120 * q^41 + 400 * q^42 - 48 * q^43 + 352 * q^44 + 592 * q^45 + 48 * q^46 + 286 * q^47 - 120 * q^48 + 110 * q^49 - 664 * q^50 - 234 * q^51 - 864 * q^52 + 136 * q^53 - 1208 * q^54 - 528 * q^55 - 576 * q^56 - 584 * q^57 - 1080 * q^58 - 622 * q^59 - 904 * q^60 - 504 * q^61 - 456 * q^62 - 498 * q^63 + 416 * q^64 - 412 * q^65 + 1136 * q^66 + 2 * q^67 + 712 * q^68 - 432 * q^69 + 640 * q^70 + 292 * q^71 + 1472 * q^72 - 8 * q^73 + 1040 * q^74 + 708 * q^75 + 1008 * q^76 - 180 * q^77 + 424 * q^78 + 1022 * q^79 - 648 * q^80 + 282 * q^81 - 1296 * q^82 + 1272 * q^83 - 1016 * q^84 - 384 * q^85 - 1400 * q^86 + 832 * q^87 - 1368 * q^88 - 200 * q^89 - 2632 * q^90 - 116 * q^91 - 1736 * q^92 - 1464 * q^93 - 2552 * q^94 - 594 * q^95 - 3368 * q^96 - 1144 * q^97 - 1880 * q^98 - 1328 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(224))\)

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
224.3.c	\(\chi_{224}(97, \cdot)\)	224.3.c.a	8	1
		224.3.c.b	8
224.3.d	\(\chi_{224}(127, \cdot)\)	224.3.d.a	4	1
		224.3.d.b	8
224.3.g	\(\chi_{224}(15, \cdot)\)	224.3.g.a	4	1
		224.3.g.b	8
224.3.h	\(\chi_{224}(209, \cdot)\)	224.3.h.a	2	1
		224.3.h.b	2
		224.3.h.c	2
		224.3.h.d	8
224.3.k	\(\chi_{224}(71, \cdot)\)	None	0	2
224.3.l	\(\chi_{224}(41, \cdot)\)	None	0	2
224.3.n	\(\chi_{224}(17, \cdot)\)	224.3.n.a	28	2
224.3.o	\(\chi_{224}(79, \cdot)\)	224.3.o.a	2	2
		224.3.o.b	2
		224.3.o.c	12
		224.3.o.d	12
224.3.r	\(\chi_{224}(95, \cdot)\)	224.3.r.a	4	2
		224.3.r.b	4
		224.3.r.c	12
		224.3.r.d	12
224.3.s	\(\chi_{224}(33, \cdot)\)	224.3.s.a	16	2
		224.3.s.b	16
224.3.v	\(\chi_{224}(13, \cdot)\)	224.3.v.a	8	4
		224.3.v.b	240
224.3.w	\(\chi_{224}(43, \cdot)\)	224.3.w.a	192	4
224.3.y	\(\chi_{224}(23, \cdot)\)	None	0	4
224.3.bb	\(\chi_{224}(73, \cdot)\)	None	0	4
224.3.bc	\(\chi_{224}(5, \cdot)\)	224.3.bc.a	496	8
224.3.bf	\(\chi_{224}(11, \cdot)\)	224.3.bf.a	496	8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(224))\) into lower level spaces

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