Space of modular forms of level 2916 and weight 2

• Label: 2916.2
• Level: 2916
• Weight: 2
• Dimension: 108216
• Nonzero newspaces: 12
• Sturm bound: 944784
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 2916 = 2^{2} \cdot 3^{6} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(944784\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2916))\).

	Total	New	Old
Modular forms	239436	109512	129924
Cusp forms	232957	108216	124741
Eisenstein series	6479	1296	5183

Trace form

108216 * q - 108 * q^2 - 180 * q^4 - 216 * q^5 - 162 * q^6 - 108 * q^8 - 324 * q^9 - 252 * q^10 - 162 * q^12 - 360 * q^13 - 108 * q^14 - 180 * q^16 - 216 * q^17 - 162 * q^18 - 108 * q^20 - 324 * q^21 - 180 * q^22 - 162 * q^24 - 360 * q^25 - 108 * q^26 - 324 * q^28 - 216 * q^29 - 162 * q^30 - 108 * q^32 - 324 * q^33 - 180 * q^34 - 162 * q^36 - 504 * q^37 - 108 * q^38 - 180 * q^40 - 216 * q^41 - 162 * q^42 - 108 * q^44 - 324 * q^45 - 252 * q^46 - 162 * q^48 - 360 * q^49 - 108 * q^50 - 180 * q^52 - 216 * q^53 - 162 * q^54 - 108 * q^56 - 324 * q^57 - 180 * q^58 - 162 * q^60 - 360 * q^61 - 108 * q^62 - 252 * q^64 - 270 * q^65 - 162 * q^66 - 54 * q^67 - 108 * q^68 - 324 * q^69 - 180 * q^70 - 108 * q^71 - 162 * q^72 - 585 * q^73 - 108 * q^74 - 180 * q^76 - 432 * q^77 - 162 * q^78 - 108 * q^79 - 81 * q^80 - 324 * q^81 - 405 * q^82 - 108 * q^83 - 162 * q^84 - 468 * q^85 - 108 * q^86 - 180 * q^88 - 351 * q^89 - 162 * q^90 - 81 * q^91 - 108 * q^92 - 324 * q^93 - 180 * q^94 - 108 * q^95 - 162 * q^96 - 414 * q^97 - 108 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2916))\)

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
2916.2.a	\(\chi_{2916}(1, \cdot)\)	2916.2.a.a	3	1
		2916.2.a.b	3
		2916.2.a.c	9
		2916.2.a.d	9
		2916.2.a.e	12
2916.2.b	\(\chi_{2916}(2915, \cdot)\)	n/a	204	1
2916.2.e	\(\chi_{2916}(973, \cdot)\)	2916.2.e.a	6	2
		2916.2.e.b	6
		2916.2.e.c	18
		2916.2.e.d	18
		2916.2.e.e	24
2916.2.h	\(\chi_{2916}(971, \cdot)\)	n/a	408	2
2916.2.i	\(\chi_{2916}(325, \cdot)\)	n/a	216	6
2916.2.l	\(\chi_{2916}(323, \cdot)\)	n/a	1260	6
2916.2.m	\(\chi_{2916}(109, \cdot)\)	n/a	648	18
2916.2.p	\(\chi_{2916}(107, \cdot)\)	n/a	3744	18
2916.2.q	\(\chi_{2916}(37, \cdot)\)	n/a	1458	54
2916.2.t	\(\chi_{2916}(35, \cdot)\)	n/a	8640	54
2916.2.u	\(\chi_{2916}(13, \cdot)\)	n/a	13122	162
2916.2.x	\(\chi_{2916}(11, \cdot)\)	n/a	78408	162

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2916))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2916)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(486))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(729))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(972))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1458))\)\(^{\oplus 2}\)