Space of modular forms of level 63 and weight 4

• Label: 63.4
• Level: 63
• Weight: 4
• Dimension: 305
• Nonzero newspaces: 10
• Newform subspaces: 20
• Sturm bound: 1152
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 20 \)
Sturm bound:			\(1152\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(63))\).

	Total	New	Old
Modular forms	480	349	131
Cusp forms	384	305	79
Eisenstein series	96	44	52

Trace form

305 * q - 3 * q^2 - 6 * q^3 + 17 * q^4 + 33 * q^5 - 30 * q^6 + 2 * q^7 - 177 * q^8 - 102 * q^9 - 78 * q^10 + 123 * q^11 + 348 * q^12 + 256 * q^13 + 603 * q^14 + 42 * q^15 - 91 * q^16 - 615 * q^17 - 780 * q^18 - 491 * q^19 - 1626 * q^20 - 393 * q^21 - 954 * q^22 - 237 * q^23 - 102 * q^24 + 209 * q^25 + 1626 * q^26 + 1248 * q^27 + 1433 * q^28 + 1140 * q^29 + 1002 * q^30 + 1345 * q^31 + 2535 * q^32 + 336 * q^33 + 1530 * q^34 - 3 * q^35 - 234 * q^36 - 1517 * q^37 - 4596 * q^38 - 2790 * q^39 - 3654 * q^40 - 2784 * q^41 - 2232 * q^42 - 788 * q^43 - 3570 * q^44 - 54 * q^45 - 1218 * q^46 - 201 * q^47 - 2502 * q^48 + 1148 * q^49 + 159 * q^50 - 1362 * q^51 + 3970 * q^52 + 2841 * q^53 + 336 * q^54 + 510 * q^55 + 4599 * q^56 + 3954 * q^57 - 2652 * q^58 + 4005 * q^59 + 8670 * q^60 - 2327 * q^61 + 3084 * q^62 + 4593 * q^63 + 1733 * q^64 + 4722 * q^65 + 8226 * q^66 + 4651 * q^67 + 12738 * q^68 + 3978 * q^69 + 9078 * q^70 - 348 * q^71 - 1920 * q^72 + 3355 * q^73 + 90 * q^74 - 5718 * q^75 - 878 * q^76 - 8508 * q^77 - 11040 * q^78 - 7793 * q^79 - 18114 * q^80 - 5346 * q^81 - 19734 * q^82 - 9438 * q^83 - 8322 * q^84 - 9918 * q^85 - 10644 * q^86 - 1182 * q^87 + 5988 * q^88 + 1893 * q^89 + 1914 * q^90 + 3070 * q^91 + 4848 * q^92 + 2094 * q^93 + 7284 * q^94 + 3339 * q^95 + 1320 * q^96 + 7912 * q^97 + 11763 * q^98 + 3366 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)

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
63.4.a	\(\chi_{63}(1, \cdot)\)	63.4.a.a	1	1
		63.4.a.b	1
		63.4.a.c	1
		63.4.a.d	2
		63.4.a.e	2
63.4.c	\(\chi_{63}(62, \cdot)\)	63.4.c.a	4	1
		63.4.c.b	4
63.4.e	\(\chi_{63}(37, \cdot)\)	63.4.e.a	2	2
		63.4.e.b	2
		63.4.e.c	6
		63.4.e.d	8
63.4.f	\(\chi_{63}(22, \cdot)\)	63.4.f.a	2	2
		63.4.f.b	16
		63.4.f.c	18
63.4.g	\(\chi_{63}(4, \cdot)\)	63.4.g.a	44	2
63.4.h	\(\chi_{63}(25, \cdot)\)	63.4.h.a	44	2
63.4.i	\(\chi_{63}(5, \cdot)\)	63.4.i.a	44	2
63.4.o	\(\chi_{63}(20, \cdot)\)	63.4.o.a	44	2
63.4.p	\(\chi_{63}(17, \cdot)\)	63.4.p.a	16	2
63.4.s	\(\chi_{63}(47, \cdot)\)	63.4.s.a	44	2

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(63))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(63)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)