Space of modular forms of level 63 and weight 7

• Label: 63.7
• Level: 63
• Weight: 7
• Dimension: 633
• Nonzero newspaces: 10
• Newform subspaces: 19
• Sturm bound: 2016
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 19 \)
Sturm bound:			\(2016\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(63))\).

	Total	New	Old
Modular forms	912	679	233
Cusp forms	816	633	183
Eisenstein series	96	46	50

Trace form

633 * q - 3 * q^2 - 60 * q^3 + 129 * q^4 + 597 * q^5 - 678 * q^6 - 1416 * q^7 - 723 * q^8 + 3948 * q^9 + 6060 * q^10 + 3141 * q^11 + 3264 * q^12 - 9780 * q^13 - 4323 * q^14 - 3954 * q^15 - 3003 * q^16 - 28065 * q^17 - 17844 * q^18 - 1335 * q^19 + 126354 * q^20 + 48153 * q^21 - 3792 * q^22 - 21291 * q^23 - 158538 * q^24 - 465 * q^25 - 87966 * q^26 + 113352 * q^27 - 128895 * q^28 + 68436 * q^29 + 65802 * q^30 + 47013 * q^31 - 46599 * q^32 - 251682 * q^33 + 22296 * q^34 + 104667 * q^35 + 276030 * q^36 - 187359 * q^37 - 291492 * q^38 - 59274 * q^39 - 913434 * q^40 - 464520 * q^41 + 67698 * q^42 + 1239948 * q^43 + 1616244 * q^44 + 534978 * q^45 + 1026642 * q^46 + 376905 * q^47 + 806526 * q^48 - 1245780 * q^49 - 2607417 * q^50 - 1936128 * q^51 - 947622 * q^52 - 1313349 * q^53 - 278628 * q^54 + 1971348 * q^55 + 2086437 * q^56 + 1123428 * q^57 - 33648 * q^58 + 2309817 * q^59 + 4881522 * q^60 - 1247067 * q^61 - 1505571 * q^63 - 1526835 * q^64 - 4573560 * q^65 - 6991146 * q^66 + 1224189 * q^67 - 1103328 * q^68 + 1080306 * q^69 + 4776654 * q^70 + 4198758 * q^71 + 4337304 * q^72 + 528873 * q^73 + 2834508 * q^74 + 4600860 * q^75 - 9264792 * q^76 - 3759558 * q^77 - 696084 * q^78 - 2724759 * q^79 - 10186266 * q^80 - 6640812 * q^81 - 1737564 * q^82 - 6016692 * q^83 + 426270 * q^84 + 4201614 * q^85 - 761982 * q^86 + 4510194 * q^87 + 14144598 * q^88 + 14490915 * q^89 + 12333246 * q^90 + 9281298 * q^91 + 17843694 * q^92 + 7050822 * q^93 - 666462 * q^94 - 8040429 * q^95 - 12259272 * q^96 - 17964816 * q^97 - 27745749 * q^98 - 8909226 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(63))\)

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
63.7.b	\(\chi_{63}(8, \cdot)\)	63.7.b.a	12	1
63.7.d	\(\chi_{63}(55, \cdot)\)	63.7.d.a	1	1
		63.7.d.b	2
		63.7.d.c	2
		63.7.d.d	2
		63.7.d.e	4
		63.7.d.f	8
63.7.j	\(\chi_{63}(11, \cdot)\)	63.7.j.a	92	2
63.7.k	\(\chi_{63}(31, \cdot)\)	63.7.k.a	92	2
63.7.l	\(\chi_{63}(13, \cdot)\)	63.7.l.a	92	2
63.7.m	\(\chi_{63}(10, \cdot)\)	63.7.m.a	2	2
		63.7.m.b	4
		63.7.m.c	8
		63.7.m.d	8
		63.7.m.e	16
63.7.n	\(\chi_{63}(2, \cdot)\)	63.7.n.a	92	2
63.7.q	\(\chi_{63}(44, \cdot)\)	63.7.q.a	32	2
63.7.r	\(\chi_{63}(29, \cdot)\)	63.7.r.a	72	2
63.7.t	\(\chi_{63}(40, \cdot)\)	63.7.t.a	92	2

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(63))\) into lower level spaces

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