Space of modular forms of level 63 and weight 2

• Label: 63.2
• Level: 63
• Weight: 2
• Dimension: 87
• Nonzero newspaces: 10
• Newform subspaces: 17
• Sturm bound: 576
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 17 \)
Sturm bound:			\(576\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(63))\).

	Total	New	Old
Modular forms	192	131	61
Cusp forms	97	87	10
Eisenstein series	95	44	51

Trace form

87 * q - 9 * q^2 - 12 * q^3 - 13 * q^4 - 12 * q^5 - 12 * q^6 - 13 * q^7 - 27 * q^8 - 12 * q^9 - 42 * q^10 - 18 * q^11 - 16 * q^13 - 3 * q^14 - 12 * q^15 + 3 * q^16 + 12 * q^17 + 12 * q^18 - 16 * q^19 + 36 * q^20 + 6 * q^21 + 6 * q^23 + 24 * q^24 - 9 * q^25 + 24 * q^26 + 6 * q^27 - 33 * q^28 - 18 * q^29 + 30 * q^30 - 10 * q^31 + 39 * q^32 + 12 * q^33 + 12 * q^34 + 24 * q^35 + 36 * q^36 - 14 * q^37 + 54 * q^38 + 24 * q^39 + 48 * q^40 + 60 * q^41 + 54 * q^42 - 8 * q^43 + 66 * q^44 + 36 * q^45 + 24 * q^46 + 18 * q^47 - 24 * q^48 + 3 * q^49 - 9 * q^50 - 12 * q^51 + 8 * q^52 - 42 * q^53 - 42 * q^54 - 48 * q^55 - 87 * q^56 - 72 * q^57 - 36 * q^58 - 96 * q^59 - 114 * q^60 - 22 * q^61 - 156 * q^62 - 96 * q^63 - 127 * q^64 - 72 * q^65 - 54 * q^66 - 12 * q^67 - 120 * q^68 - 36 * q^69 + 24 * q^70 - 12 * q^71 - 66 * q^72 + 14 * q^73 + 12 * q^74 + 38 * q^76 + 36 * q^77 + 12 * q^78 + 36 * q^79 + 36 * q^80 + 72 * q^81 + 18 * q^82 + 66 * q^83 + 132 * q^84 + 24 * q^85 + 126 * q^86 + 78 * q^87 + 78 * q^88 + 132 * q^89 + 150 * q^90 + 38 * q^91 + 132 * q^92 + 102 * q^93 + 90 * q^94 + 114 * q^95 + 168 * q^96 + 56 * q^97 + 123 * q^98 + 72 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)

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
63.2.a	\(\chi_{63}(1, \cdot)\)	63.2.a.a	1	1
		63.2.a.b	2
63.2.c	\(\chi_{63}(62, \cdot)\)	63.2.c.a	4	1
63.2.e	\(\chi_{63}(37, \cdot)\)	63.2.e.a	2	2
		63.2.e.b	2
63.2.f	\(\chi_{63}(22, \cdot)\)	63.2.f.a	6	2
		63.2.f.b	6
63.2.g	\(\chi_{63}(4, \cdot)\)	63.2.g.a	2	2
		63.2.g.b	10
63.2.h	\(\chi_{63}(25, \cdot)\)	63.2.h.a	2	2
		63.2.h.b	10
63.2.i	\(\chi_{63}(5, \cdot)\)	63.2.i.a	2	2
		63.2.i.b	10
63.2.o	\(\chi_{63}(20, \cdot)\)	63.2.o.a	12	2
63.2.p	\(\chi_{63}(17, \cdot)\)	63.2.p.a	4	2
63.2.s	\(\chi_{63}(47, \cdot)\)	63.2.s.a	2	2
		63.2.s.b	10

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(63))\) into lower level spaces

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