Space of modular forms of level 2166 and weight 2

• Label: 2166.2
• Level: 2166
• Weight: 2
• Dimension: 32309
• Nonzero newspaces: 12
• Sturm bound: 519840
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(519840\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2166))\).

	Total	New	Old
Modular forms	131976	32309	99667
Cusp forms	127945	32309	95636
Eisenstein series	4031	0	4031

Trace form

32309 * q - q^2 - q^3 - q^4 - 6 * q^5 - q^6 - 8 * q^7 - q^8 - q^9 - 6 * q^10 - 12 * q^11 + 11 * q^12 + 82 * q^13 + 64 * q^14 + 66 * q^15 - q^16 + 54 * q^17 - q^18 + 84 * q^19 + 66 * q^20 + 76 * q^21 + 96 * q^22 + 48 * q^23 - q^24 + 113 * q^25 + 58 * q^26 + 29 * q^27 + 16 * q^28 + 42 * q^29 - 6 * q^30 + 40 * q^31 - q^32 + 96 * q^33 - 18 * q^34 + 96 * q^35 - q^36 + 34 * q^37 + 94 * q^39 - 6 * q^40 + 30 * q^41 - 8 * q^42 + 100 * q^43 - 12 * q^44 - 6 * q^45 - 24 * q^46 + 24 * q^47 - 19 * q^48 + 15 * q^49 - 31 * q^50 - 180 * q^51 - 14 * q^52 - 54 * q^53 - 109 * q^54 - 72 * q^55 - 8 * q^56 - 90 * q^57 - 30 * q^58 - 60 * q^59 - 78 * q^60 - 38 * q^61 - 32 * q^62 - 140 * q^63 - q^64 - 12 * q^65 - 156 * q^66 + 76 * q^67 - 18 * q^68 - 132 * q^69 - 48 * q^70 - 19 * q^72 + 34 * q^73 - 38 * q^74 + 53 * q^75 + 48 * q^77 + 58 * q^78 + 232 * q^79 - 6 * q^80 + 143 * q^81 + 102 * q^82 + 204 * q^83 + 100 * q^84 + 180 * q^85 + 100 * q^86 + 330 * q^87 - 12 * q^88 + 198 * q^89 + 174 * q^90 + 272 * q^91 + 120 * q^92 + 268 * q^93 + 240 * q^94 + 108 * q^95 - q^96 + 118 * q^97 + 231 * q^98 + 150 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2166))\)

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
2166.2.a	\(\chi_{2166}(1, \cdot)\)	2166.2.a.a	1	1
		2166.2.a.b	1
		2166.2.a.c	1
		2166.2.a.d	1
		2166.2.a.e	1
		2166.2.a.f	1
		2166.2.a.g	1
		2166.2.a.h	1
		2166.2.a.i	1
		2166.2.a.j	2
		2166.2.a.k	2
		2166.2.a.l	2
		2166.2.a.m	2
		2166.2.a.n	3
		2166.2.a.o	3
		2166.2.a.p	3
		2166.2.a.q	3
		2166.2.a.r	3
		2166.2.a.s	3
		2166.2.a.t	3
		2166.2.a.u	3
		2166.2.a.v	4
		2166.2.a.w	4
		2166.2.a.x	4
		2166.2.a.y	4
2166.2.b	\(\chi_{2166}(2165, \cdot)\)	n/a	112	1
2166.2.e	\(\chi_{2166}(1375, \cdot)\)	n/a	116	2
2166.2.h	\(\chi_{2166}(293, \cdot)\)	n/a	224	2
2166.2.i	\(\chi_{2166}(415, \cdot)\)	n/a	336	6
2166.2.l	\(\chi_{2166}(299, \cdot)\)	n/a	684	6
2166.2.m	\(\chi_{2166}(115, \cdot)\)	n/a	1116	18
2166.2.p	\(\chi_{2166}(113, \cdot)\)	n/a	2304	18
2166.2.q	\(\chi_{2166}(7, \cdot)\)	n/a	2232	36
2166.2.r	\(\chi_{2166}(65, \cdot)\)	n/a	4608	36
2166.2.u	\(\chi_{2166}(25, \cdot)\)	n/a	6912	108
2166.2.v	\(\chi_{2166}(29, \cdot)\)	n/a	13608	108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2166))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2166)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 2}\)