Space of modular forms of level 63 and weight 8

• Label: 63.8
• Level: 63
• Weight: 8
• Dimension: 741
• Nonzero newspaces: 10
• Newform subspaces: 23
• Sturm bound: 2304
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 23 \)
Sturm bound:			\(2304\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(63))\).

	Total	New	Old
Modular forms	1056	785	271
Cusp forms	960	741	219
Eisenstein series	96	44	52

Trace form

741 * q + 21 * q^2 - 60 * q^3 - 367 * q^4 + 1128 * q^5 + 2454 * q^6 - 49 * q^7 - 16329 * q^8 - 1992 * q^9 + 8742 * q^10 + 16266 * q^11 - 15348 * q^12 + 17648 * q^13 - 44973 * q^14 - 8148 * q^15 + 60909 * q^16 + 87132 * q^17 - 72132 * q^18 - 251956 * q^19 - 190866 * q^20 + 66270 * q^21 + 280626 * q^22 + 124266 * q^23 + 103578 * q^24 + 162309 * q^25 - 520098 * q^26 - 857730 * q^27 - 901839 * q^28 + 179058 * q^29 + 2848962 * q^30 + 492290 * q^31 - 128913 * q^32 - 457944 * q^33 - 1091466 * q^34 + 656652 * q^35 - 1951506 * q^36 + 2744074 * q^37 + 4772940 * q^38 + 3183264 * q^39 - 3455574 * q^40 - 3367428 * q^41 - 4743936 * q^42 - 4626656 * q^43 - 7777794 * q^44 - 2986164 * q^45 + 11345502 * q^46 + 9661350 * q^47 + 18001386 * q^48 + 2084193 * q^49 + 7729959 * q^50 - 2021340 * q^51 - 23902198 * q^52 - 14443530 * q^53 - 22723620 * q^54 + 583560 * q^55 - 4716657 * q^56 - 559860 * q^57 + 21151572 * q^58 + 9328356 * q^59 + 18712830 * q^60 - 5806786 * q^61 + 2740116 * q^62 + 21268740 * q^63 - 14293123 * q^64 + 4668312 * q^65 - 14645214 * q^66 + 11242056 * q^67 - 24928806 * q^68 - 31955220 * q^69 - 14506062 * q^70 - 36266124 * q^71 - 4366560 * q^72 + 34110566 * q^73 + 41871978 * q^74 + 31179552 * q^75 + 21971426 * q^76 + 51871944 * q^77 + 40058328 * q^78 - 5264592 * q^79 + 5389566 * q^80 + 25124436 * q^81 - 61795854 * q^82 - 78860982 * q^83 - 87895482 * q^84 - 38081568 * q^85 - 75120384 * q^86 - 18502338 * q^87 + 46814004 * q^88 + 42374004 * q^89 + 59804394 * q^90 + 44643062 * q^91 + 33357216 * q^92 + 16669806 * q^93 + 50282580 * q^94 + 74383254 * q^95 + 51168984 * q^96 + 47727560 * q^97 + 54792135 * q^98 + 32862960 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(63))\)

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
63.8.a	\(\chi_{63}(1, \cdot)\)	63.8.a.a	1	1
		63.8.a.b	1
		63.8.a.c	2
		63.8.a.d	2
		63.8.a.e	2
		63.8.a.f	2
		63.8.a.g	3
		63.8.a.h	4
63.8.c	\(\chi_{63}(62, \cdot)\)	63.8.c.a	4	1
		63.8.c.b	16
63.8.e	\(\chi_{63}(37, \cdot)\)	63.8.e.a	2	2
		63.8.e.b	8
		63.8.e.c	8
		63.8.e.d	10
		63.8.e.e	16
63.8.f	\(\chi_{63}(22, \cdot)\)	63.8.f.a	42	2
		63.8.f.b	42
63.8.g	\(\chi_{63}(4, \cdot)\)	63.8.g.a	108	2
63.8.h	\(\chi_{63}(25, \cdot)\)	63.8.h.a	108	2
63.8.i	\(\chi_{63}(5, \cdot)\)	63.8.i.a	108	2
63.8.o	\(\chi_{63}(20, \cdot)\)	63.8.o.a	108	2
63.8.p	\(\chi_{63}(17, \cdot)\)	63.8.p.a	36	2
63.8.s	\(\chi_{63}(47, \cdot)\)	63.8.s.a	108	2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(63))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(63)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)