Space of modular forms of level 63 and weight 3

• Label: 63.3
• Level: 63
• Weight: 3
• Dimension: 197
• Nonzero newspaces: 10
• Newform subspaces: 18
• Sturm bound: 864
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 18 \)
Sturm bound:			\(864\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(63))\).

	Total	New	Old
Modular forms	336	243	93
Cusp forms	240	197	43
Eisenstein series	96	46	50

Trace form

197 * q - 3 * q^2 - 6 * q^3 + q^4 - 18 * q^5 - 30 * q^6 - 11 * q^7 - 15 * q^8 + 6 * q^9 - 6 * q^11 - 48 * q^12 - 42 * q^13 - 135 * q^14 - 84 * q^15 - 199 * q^16 - 114 * q^17 - 60 * q^18 - 96 * q^19 - 6 * q^20 + 12 * q^21 + 96 * q^22 + 216 * q^23 + 222 * q^24 + 185 * q^25 + 234 * q^26 + 6 * q^27 + 257 * q^28 - 6 * q^29 - 78 * q^30 - 138 * q^31 - 363 * q^32 - 222 * q^33 - 456 * q^34 - 438 * q^35 - 306 * q^36 - 118 * q^37 - 300 * q^38 - 36 * q^39 - 234 * q^40 + 24 * q^41 + 54 * q^42 + 20 * q^43 + 408 * q^44 + 288 * q^45 + 330 * q^46 + 594 * q^47 + 774 * q^48 + 203 * q^49 + 1203 * q^50 + 582 * q^51 + 378 * q^52 + 834 * q^53 + 1092 * q^54 + 168 * q^55 + 993 * q^56 + 282 * q^57 + 72 * q^58 - 90 * q^59 + 282 * q^60 + 60 * q^61 - 132 * q^63 + 241 * q^64 - 480 * q^65 - 522 * q^66 - 212 * q^67 - 1332 * q^68 - 936 * q^69 - 786 * q^70 - 1266 * q^71 - 2208 * q^72 - 900 * q^73 - 2040 * q^74 - 1290 * q^75 - 432 * q^76 - 1104 * q^77 - 1284 * q^78 - 302 * q^79 - 1266 * q^80 - 18 * q^81 - 300 * q^82 + 150 * q^83 - 114 * q^84 + 384 * q^85 + 450 * q^86 + 438 * q^87 - 258 * q^88 + 102 * q^89 + 6 * q^90 + 264 * q^91 - 234 * q^92 - 138 * q^93 + 450 * q^94 + 726 * q^95 + 384 * q^96 + 492 * q^97 + 963 * q^98 + 504 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(63))\)

We only show spaces with odd 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
63.3.b	\(\chi_{63}(8, \cdot)\)	63.3.b.a	4	1
63.3.d	\(\chi_{63}(55, \cdot)\)	63.3.d.a	1	1
		63.3.d.b	2
		63.3.d.c	2
63.3.j	\(\chi_{63}(11, \cdot)\)	63.3.j.a	6	2
		63.3.j.b	22
63.3.k	\(\chi_{63}(31, \cdot)\)	63.3.k.a	28	2
63.3.l	\(\chi_{63}(13, \cdot)\)	63.3.l.a	28	2
63.3.m	\(\chi_{63}(10, \cdot)\)	63.3.m.a	2	2
		63.3.m.b	2
		63.3.m.c	2
		63.3.m.d	2
		63.3.m.e	4
63.3.n	\(\chi_{63}(2, \cdot)\)	63.3.n.a	6	2
		63.3.n.b	22
63.3.q	\(\chi_{63}(44, \cdot)\)	63.3.q.a	12	2
63.3.r	\(\chi_{63}(29, \cdot)\)	63.3.r.a	24	2
63.3.t	\(\chi_{63}(40, \cdot)\)	63.3.t.a	28	2

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(63))\) into lower level spaces

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