Space of modular forms of level 486 and weight 2

• Label: 486.2
• Level: 486
• Weight: 2
• Dimension: 1728
• Nonzero newspaces: 5
• Newform subspaces: 28
• Sturm bound: 26244
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 486 = 2 \cdot 3^{5} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 28 \)
Sturm bound:			\(26244\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(486))\).

	Total	New	Old
Modular forms	6939	1728	5211
Cusp forms	6184	1728	4456
Eisenstein series	755	0	755

Trace form

1728 * q + 18 * q^19 + 18 * q^20 + 18 * q^22 + 54 * q^23 + 36 * q^25 + 54 * q^26 + 18 * q^28 + 54 * q^29 + 36 * q^31 + 18 * q^34 + 54 * q^35 + 18 * q^37 + 9 * q^38 + 18 * q^41 + 18 * q^43 + 54 * q^47 + 36 * q^49 + 54 * q^53 + 54 * q^55 + 63 * q^59 + 36 * q^61 - 126 * q^65 - 108 * q^66 - 108 * q^67 - 45 * q^68 - 216 * q^69 - 126 * q^70 - 360 * q^71 - 108 * q^72 - 216 * q^73 - 360 * q^74 - 270 * q^75 - 63 * q^76 - 720 * q^77 - 216 * q^78 - 252 * q^79 - 90 * q^80 - 216 * q^81 - 216 * q^82 - 360 * q^83 - 54 * q^84 - 252 * q^85 - 360 * q^86 - 432 * q^87 - 63 * q^88 - 441 * q^89 - 216 * q^90 - 198 * q^91 - 180 * q^92 - 216 * q^93 - 126 * q^94 - 306 * q^95 - 27 * q^96 - 108 * q^97 - 180 * q^98 - 108 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(486))\)

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
486.2.a	\(\chi_{486}(1, \cdot)\)	486.2.a.a	1	1
		486.2.a.b	1
		486.2.a.c	1
		486.2.a.d	1
		486.2.a.e	1
		486.2.a.f	1
		486.2.a.g	3
		486.2.a.h	3
486.2.c	\(\chi_{486}(163, \cdot)\)	486.2.c.a	2	2
		486.2.c.b	2
		486.2.c.c	2
		486.2.c.d	2
		486.2.c.e	2
		486.2.c.f	2
		486.2.c.g	6
		486.2.c.h	6
486.2.e	\(\chi_{486}(55, \cdot)\)	486.2.e.a	6	6
		486.2.e.b	6
		486.2.e.c	6
		486.2.e.d	6
		486.2.e.e	12
		486.2.e.f	12
		486.2.e.g	12
		486.2.e.h	12
486.2.g	\(\chi_{486}(19, \cdot)\)	486.2.g.a	72	18
		486.2.g.b	90
486.2.i	\(\chi_{486}(7, \cdot)\)	486.2.i.a	702	54
		486.2.i.b	756

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(486))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(486)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 2}\)