Space of modular forms of level 648 and weight 3

• Label: 648.3
• Level: 648
• Weight: 3
• Dimension: 10256
• Nonzero newspaces: 12
• Sturm bound: 69984
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(69984\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(648))\).

	Total	New	Old
Modular forms	23976	10480	13496
Cusp forms	22680	10256	12424
Eisenstein series	1296	224	1072

Trace form

10256 * 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 - 6 * q^11 - 36 * q^12 + 24 * q^13 - 24 * q^14 - 36 * q^15 - 40 * q^16 - 48 * q^17 - 36 * q^18 - 70 * q^19 - 24 * q^20 - 56 * q^22 - 96 * q^23 - 36 * q^24 - 128 * q^25 - 186 * q^26 - 36 * q^27 - 226 * q^28 - 108 * q^29 - 36 * q^30 - 112 * q^31 - 204 * q^32 - 72 * q^33 - 76 * q^34 - 30 * q^35 - 36 * q^36 + 36 * q^37 + 156 * q^38 - 36 * q^39 + 140 * q^40 - 354 * q^41 - 36 * q^42 - 106 * q^43 + 408 * q^44 - 432 * q^45 + 222 * q^46 - 348 * q^47 - 36 * q^48 - 248 * q^49 + 126 * q^50 - 162 * q^51 + 24 * q^52 - 36 * q^54 - 14 * q^55 + 270 * q^56 + 144 * q^57 + 272 * q^58 + 174 * q^59 - 36 * q^60 + 156 * q^61 + 570 * q^62 + 504 * q^63 + 194 * q^64 + 816 * q^65 - 36 * q^66 + 62 * q^67 + 210 * q^68 + 288 * q^69 + 88 * q^70 - 18 * q^71 - 36 * q^72 + 16 * q^73 - 252 * q^74 - 36 * q^75 - 400 * q^76 + 504 * q^77 + 126 * q^78 + 524 * q^79 - 834 * q^80 - 72 * q^81 - 508 * q^82 + 876 * q^83 - 36 * q^84 + 324 * q^85 - 924 * q^86 - 36 * q^87 + 448 * q^88 + 924 * q^89 + 2106 * q^90 + 1242 * q^91 + 4476 * q^92 + 756 * q^93 + 1614 * q^94 + 3186 * q^95 + 2538 * q^96 + 406 * q^97 + 5106 * q^98 + 1260 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(648))\)

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
648.3.b	\(\chi_{648}(163, \cdot)\)	648.3.b.a	2	1
		648.3.b.b	2
		648.3.b.c	12
		648.3.b.d	12
		648.3.b.e	20
		648.3.b.f	20
		648.3.b.g	24
648.3.e	\(\chi_{648}(161, \cdot)\)	648.3.e.a	4	1
		648.3.e.b	4
		648.3.e.c	8
		648.3.e.d	8
648.3.g	\(\chi_{648}(487, \cdot)\)	None	0	1
648.3.h	\(\chi_{648}(485, \cdot)\)	648.3.h.a	44	1
		648.3.h.b	48
648.3.j	\(\chi_{648}(53, \cdot)\)	n/a	188	2
648.3.k	\(\chi_{648}(55, \cdot)\)	None	0	2
648.3.m	\(\chi_{648}(377, \cdot)\)	648.3.m.a	4	2
		648.3.m.b	4
		648.3.m.c	4
		648.3.m.d	4
		648.3.m.e	8
		648.3.m.f	8
		648.3.m.g	16
648.3.p	\(\chi_{648}(379, \cdot)\)	n/a	188	2
648.3.r	\(\chi_{648}(19, \cdot)\)	n/a	420	6
648.3.s	\(\chi_{648}(127, \cdot)\)	None	0	6
648.3.u	\(\chi_{648}(17, \cdot)\)	n/a	108	6
648.3.x	\(\chi_{648}(125, \cdot)\)	n/a	420	6
648.3.z	\(\chi_{648}(5, \cdot)\)	n/a	3852	18
648.3.ba	\(\chi_{648}(7, \cdot)\)	None	0	18
648.3.bc	\(\chi_{648}(41, \cdot)\)	n/a	972	18
648.3.bf	\(\chi_{648}(43, \cdot)\)	n/a	3852	18

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(648))\) into lower level spaces

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