Space of modular forms of level 63 and weight 6

• Label: 63.6
• Level: 63
• Weight: 6
• Dimension: 525
• Nonzero newspaces: 10
• Newform subspaces: 25
• Sturm bound: 1728
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 25 \)
Sturm bound:			\(1728\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(63))\).

	Total	New	Old
Modular forms	768	569	199
Cusp forms	672	525	147
Eisenstein series	96	44	52

Trace form

525 * q - 27 * q^2 + 12 * q^3 + 145 * q^4 - 186 * q^5 - 354 * q^6 - 113 * q^7 + 1647 * q^8 + 816 * q^9 + 1470 * q^10 - 1818 * q^11 - 5268 * q^12 - 620 * q^13 - 3381 * q^14 + 780 * q^15 - 3795 * q^16 + 9690 * q^17 + 19164 * q^18 + 4720 * q^19 + 10782 * q^20 - 1860 * q^21 + 2706 * q^22 - 15846 * q^23 - 12630 * q^24 - 13119 * q^25 + 4638 * q^26 + 5190 * q^27 - 18639 * q^28 - 10242 * q^29 - 2670 * q^30 + 34978 * q^31 - 14457 * q^32 - 9996 * q^33 - 75426 * q^34 - 45312 * q^35 - 17586 * q^36 + 12644 * q^37 + 54468 * q^38 + 22032 * q^39 + 200994 * q^40 + 128136 * q^41 + 98064 * q^42 + 40136 * q^43 - 14754 * q^44 - 80280 * q^45 - 174642 * q^46 - 106362 * q^47 - 119574 * q^48 - 110745 * q^49 - 218601 * q^50 - 32628 * q^51 - 142838 * q^52 + 170700 * q^53 + 348420 * q^54 + 131544 * q^55 + 312495 * q^56 + 227820 * q^57 + 151140 * q^58 - 80256 * q^59 - 586050 * q^60 - 9632 * q^61 - 727836 * q^62 - 451140 * q^63 + 128653 * q^64 + 14364 * q^65 + 111474 * q^66 + 295692 * q^67 + 779610 * q^68 + 524592 * q^69 - 592710 * q^70 - 164652 * q^71 + 282480 * q^72 - 761612 * q^73 - 247206 * q^74 - 69096 * q^75 - 289310 * q^76 - 183132 * q^77 - 853080 * q^78 + 664872 * q^79 + 319374 * q^80 + 81684 * q^81 + 1371642 * q^82 + 809898 * q^83 + 673230 * q^84 + 779916 * q^85 + 1375056 * q^86 + 830526 * q^87 + 553908 * q^88 + 617538 * q^89 + 461274 * q^90 - 977354 * q^91 - 2770368 * q^92 - 1333578 * q^93 - 3026628 * q^94 - 2712642 * q^95 - 1430616 * q^96 - 773204 * q^97 - 606201 * q^98 + 43272 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(63))\)

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
63.6.a	\(\chi_{63}(1, \cdot)\)	63.6.a.a	1	1
		63.6.a.b	1
		63.6.a.c	1
		63.6.a.d	1
		63.6.a.e	1
		63.6.a.f	2
		63.6.a.g	2
		63.6.a.h	4
63.6.c	\(\chi_{63}(62, \cdot)\)	63.6.c.a	4	1
		63.6.c.b	8
63.6.e	\(\chi_{63}(37, \cdot)\)	63.6.e.a	2	2
		63.6.e.b	2
		63.6.e.c	4
		63.6.e.d	4
		63.6.e.e	8
		63.6.e.f	12
63.6.f	\(\chi_{63}(22, \cdot)\)	63.6.f.a	30	2
		63.6.f.b	30
63.6.g	\(\chi_{63}(4, \cdot)\)	63.6.g.a	76	2
63.6.h	\(\chi_{63}(25, \cdot)\)	63.6.h.a	76	2
63.6.i	\(\chi_{63}(5, \cdot)\)	63.6.i.a	76	2
63.6.o	\(\chi_{63}(20, \cdot)\)	63.6.o.a	76	2
63.6.p	\(\chi_{63}(17, \cdot)\)	63.6.p.a	4	2
		63.6.p.b	24
63.6.s	\(\chi_{63}(47, \cdot)\)	63.6.s.a	76	2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(63))\) into lower level spaces

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