Space of modular forms of level 648 and weight 2

• Label: 648.2
• Level: 648
• Weight: 2
• Dimension: 5072
• Nonzero newspaces: 12
• Newform subspaces: 66
• Sturm bound: 46656
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 66 \)
Sturm bound:			\(46656\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(648))\).

	Total	New	Old
Modular forms	12312	5296	7016
Cusp forms	11017	5072	5945
Eisenstein series	1295	224	1071

Trace form

5072 * q - 24 * q^2 - 36 * q^3 - 40 * q^4 - 36 * q^6 - 40 * q^7 - 24 * q^8 - 72 * q^9 - 58 * q^10 - 27 * q^11 - 36 * q^12 - 6 * q^13 - 24 * q^14 - 36 * q^15 - 40 * q^16 - 60 * q^17 - 36 * q^18 - 64 * q^19 - 24 * q^20 - 32 * q^22 - 36 * q^23 - 36 * q^24 - 86 * q^25 - 6 * q^26 - 36 * q^27 - 34 * q^28 + 18 * q^29 - 36 * q^30 - 22 * q^31 + 36 * q^32 - 72 * q^33 - 4 * q^34 + 18 * q^35 - 36 * q^36 + 18 * q^37 + 36 * q^38 - 36 * q^39 - 4 * q^40 - 9 * q^41 - 36 * q^42 - q^43 + 24 * q^44 + 54 * q^45 - 42 * q^46 + 84 * q^47 - 36 * q^48 - 38 * q^49 + 6 * q^50 + 27 * q^51 - 24 * q^52 + 90 * q^53 - 36 * q^54 + 34 * q^55 - 66 * q^56 - 18 * q^57 - 64 * q^58 + 117 * q^59 - 36 * q^60 + 60 * q^61 - 90 * q^62 + 18 * q^63 - 94 * q^64 + 78 * q^65 - 36 * q^66 + 29 * q^67 - 102 * q^68 + 18 * q^69 - 140 * q^70 + 54 * q^71 - 36 * q^72 - 104 * q^73 - 96 * q^74 - 36 * q^75 - 112 * q^76 + 12 * q^77 - 90 * q^78 - 10 * q^79 - 114 * q^80 - 72 * q^81 - 148 * q^82 + 6 * q^83 - 36 * q^84 - 84 * q^86 - 36 * q^87 - 176 * q^88 - 120 * q^89 - 162 * q^90 - 126 * q^91 - 324 * q^92 - 54 * q^93 - 174 * q^94 - 294 * q^95 - 270 * q^96 - 161 * q^97 - 594 * q^98 - 198 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(648))\)

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
648.2.a	\(\chi_{648}(1, \cdot)\)	648.2.a.a	1	1
		648.2.a.b	1
		648.2.a.c	1
		648.2.a.d	1
		648.2.a.e	2
		648.2.a.f	2
		648.2.a.g	2
		648.2.a.h	2
648.2.c	\(\chi_{648}(647, \cdot)\)	None	0	1
648.2.d	\(\chi_{648}(325, \cdot)\)	648.2.d.a	2	1
		648.2.d.b	2
		648.2.d.c	2
		648.2.d.d	2
		648.2.d.e	4
		648.2.d.f	4
		648.2.d.g	4
		648.2.d.h	4
		648.2.d.i	4
		648.2.d.j	8
		648.2.d.k	8
648.2.f	\(\chi_{648}(323, \cdot)\)	648.2.f.a	4	1
		648.2.f.b	16
		648.2.f.c	24
648.2.i	\(\chi_{648}(217, \cdot)\)	648.2.i.a	2	2
		648.2.i.b	2
		648.2.i.c	2
		648.2.i.d	2
		648.2.i.e	2
		648.2.i.f	2
		648.2.i.g	2
		648.2.i.h	2
		648.2.i.i	4
		648.2.i.j	4
648.2.l	\(\chi_{648}(107, \cdot)\)	648.2.l.a	4	2
		648.2.l.b	4
		648.2.l.c	4
		648.2.l.d	8
		648.2.l.e	8
		648.2.l.f	16
		648.2.l.g	48
648.2.n	\(\chi_{648}(109, \cdot)\)	648.2.n.a	4	2
		648.2.n.b	4
		648.2.n.c	4
		648.2.n.d	4
		648.2.n.e	4
		648.2.n.f	4
		648.2.n.g	4
		648.2.n.h	4
		648.2.n.i	4
		648.2.n.j	4
		648.2.n.k	4
		648.2.n.l	4
		648.2.n.m	4
		648.2.n.n	8
		648.2.n.o	8
		648.2.n.p	8
		648.2.n.q	16
648.2.o	\(\chi_{648}(215, \cdot)\)	None	0	2
648.2.q	\(\chi_{648}(73, \cdot)\)	648.2.q.a	24	6
		648.2.q.b	30
648.2.t	\(\chi_{648}(37, \cdot)\)	648.2.t.a	204	6
648.2.v	\(\chi_{648}(35, \cdot)\)	648.2.v.a	12	6
		648.2.v.b	192
648.2.w	\(\chi_{648}(71, \cdot)\)	None	0	6
648.2.y	\(\chi_{648}(25, \cdot)\)	648.2.y.a	234	18
		648.2.y.b	252
648.2.bb	\(\chi_{648}(11, \cdot)\)	648.2.bb.a	36	18
		648.2.bb.b	1872
648.2.bd	\(\chi_{648}(13, \cdot)\)	648.2.bd.a	1908	18
648.2.be	\(\chi_{648}(23, \cdot)\)	None	0	18

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(648))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(648)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(648))\)\(^{\oplus 1}\)