Space of modular forms of level 63 and weight 10

• Label: 63.10
• Level: 63
• Weight: 10
• Dimension: 961
• Nonzero newspaces: 10
• Newform subspaces: 22
• Sturm bound: 2880
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 22 \)
Sturm bound:			\(2880\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(63))\).

	Total	New	Old
Modular forms	1344	1005	339
Cusp forms	1248	961	287
Eisenstein series	96	44	52

Trace form

961 * q - 75 * q^2 - 6 * q^3 + 3409 * q^4 - 5751 * q^5 - 4890 * q^6 + 9634 * q^7 + 35103 * q^8 + 31326 * q^9 - 91770 * q^10 - 79005 * q^11 + 485484 * q^12 - 37756 * q^13 - 808485 * q^14 - 652710 * q^15 + 1295245 * q^16 - 960099 * q^17 + 678540 * q^18 + 1977965 * q^19 + 4525662 * q^20 + 2453583 * q^21 - 7530054 * q^22 - 12489885 * q^23 - 5097270 * q^24 + 12021061 * q^25 + 20479014 * q^26 + 24428256 * q^27 - 14114543 * q^28 - 18709500 * q^29 - 63988350 * q^30 - 5343127 * q^31 - 9137481 * q^32 + 71455404 * q^33 + 52946310 * q^34 - 2401227 * q^35 + 14912622 * q^36 - 28562233 * q^37 - 156496380 * q^38 - 138670902 * q^39 + 92936754 * q^40 + 51663492 * q^41 + 132958512 * q^42 + 133774340 * q^43 + 601946910 * q^44 + 91184130 * q^45 - 482632002 * q^46 - 502200129 * q^47 - 725124438 * q^48 - 188080340 * q^49 + 627319959 * q^50 + 277356894 * q^51 + 836518058 * q^52 + 429138093 * q^53 + 339563676 * q^54 - 80973906 * q^55 + 627554319 * q^56 - 628465002 * q^57 - 1412126652 * q^58 - 758248707 * q^59 + 119193150 * q^60 + 1049707409 * q^61 + 1072631700 * q^62 - 424628511 * q^63 + 1542998029 * q^64 - 896217726 * q^65 - 2600541486 * q^66 - 1108453813 * q^67 - 1025477958 * q^68 + 1129671450 * q^69 + 123633810 * q^70 + 3675957252 * q^71 + 2516102160 * q^72 + 1068062135 * q^73 - 1035687414 * q^74 - 4544874246 * q^75 - 5544183646 * q^76 - 2904875256 * q^77 - 239101224 * q^78 - 855628129 * q^79 + 3754659054 * q^80 + 4070282346 * q^81 + 5693296602 * q^82 + 1638929250 * q^83 + 3425088990 * q^84 + 3057900066 * q^85 + 376698216 * q^86 - 4349701182 * q^87 - 14951865420 * q^88 - 3720878823 * q^89 - 4063899846 * q^90 - 145316482 * q^91 + 7060533696 * q^92 + 4921287126 * q^93 + 16477810236 * q^94 + 7260586923 * q^95 - 711876792 * q^96 - 3436439380 * q^97 - 16937674737 * q^98 - 10536467562 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(63))\)

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
63.10.a	\(\chi_{63}(1, \cdot)\)	63.10.a.a	1	1
		63.10.a.b	2
		63.10.a.c	2
		63.10.a.d	2
		63.10.a.e	3
		63.10.a.f	3
		63.10.a.g	4
		63.10.a.h	6
63.10.c	\(\chi_{63}(62, \cdot)\)	63.10.c.a	4	1
		63.10.c.b	20
63.10.e	\(\chi_{63}(37, \cdot)\)	63.10.e.a	10	2
		63.10.e.b	10
		63.10.e.c	14
		63.10.e.d	24
63.10.f	\(\chi_{63}(22, \cdot)\)	63.10.f.a	54	2
		63.10.f.b	54
63.10.g	\(\chi_{63}(4, \cdot)\)	63.10.g.a	140	2
63.10.h	\(\chi_{63}(25, \cdot)\)	63.10.h.a	140	2
63.10.i	\(\chi_{63}(5, \cdot)\)	63.10.i.a	140	2
63.10.o	\(\chi_{63}(20, \cdot)\)	63.10.o.a	140	2
63.10.p	\(\chi_{63}(17, \cdot)\)	63.10.p.a	48	2
63.10.s	\(\chi_{63}(47, \cdot)\)	63.10.s.a	140	2

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(63))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(63)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)