Space of modular forms of level 1734 and weight 2

• Label: 1734.2
• Level: 1734
• Weight: 2
• Dimension: 20663
• Nonzero newspaces: 10
• Sturm bound: 332928
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 10 \)
Sturm bound:			\(332928\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1734))\).

	Total	New	Old
Modular forms	84832	20663	64169
Cusp forms	81633	20663	60970
Eisenstein series	3199	0	3199

Trace form

20663 * q - q^2 - q^3 - q^4 - 6 * q^5 - q^6 - 8 * q^7 - q^8 - q^9 + 10 * q^10 + 52 * q^11 + 15 * q^12 + 50 * q^13 + 56 * q^14 + 90 * q^15 + 15 * q^16 + 32 * q^17 + 63 * q^18 + 44 * q^19 + 10 * q^20 + 88 * q^21 + 52 * q^22 + 40 * q^23 + 15 * q^24 + 113 * q^25 + 2 * q^26 - q^27 - 8 * q^28 + 50 * q^29 - 6 * q^30 + 96 * q^31 - q^32 + 52 * q^33 + 80 * q^35 - q^36 + 90 * q^37 - 20 * q^38 - 14 * q^39 - 6 * q^40 + 38 * q^41 - 104 * q^42 + 52 * q^43 - 12 * q^44 - 118 * q^45 - 24 * q^46 - 48 * q^47 - q^48 - 57 * q^49 - 31 * q^50 - 64 * q^51 - 14 * q^52 - 38 * q^53 - 113 * q^54 - 8 * q^55 - 8 * q^56 - 164 * q^57 - 30 * q^58 + 4 * q^59 - 70 * q^60 + 2 * q^61 - 32 * q^62 - 8 * q^63 - q^64 - 68 * q^65 - 28 * q^66 - 4 * q^67 + 8 * q^68 + 104 * q^69 + 80 * q^70 + 120 * q^71 + 15 * q^72 + 262 * q^73 + 106 * q^74 + 193 * q^75 - 20 * q^76 + 224 * q^77 + 114 * q^78 + 240 * q^79 + 58 * q^80 + 15 * q^81 + 230 * q^82 + 172 * q^83 + 56 * q^84 + 200 * q^85 + 84 * q^86 + 66 * q^87 + 116 * q^88 + 102 * q^89 + 10 * q^90 + 272 * q^91 + 40 * q^92 - 32 * q^93 + 208 * q^94 + 136 * q^95 - q^96 + 158 * q^97 + 87 * q^98 - 28 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1734))\)

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
1734.2.a	\(\chi_{1734}(1, \cdot)\)	1734.2.a.a	1	1
		1734.2.a.b	1
		1734.2.a.c	1
		1734.2.a.d	1
		1734.2.a.e	1
		1734.2.a.f	1
		1734.2.a.g	1
		1734.2.a.h	1
		1734.2.a.i	1
		1734.2.a.j	1
		1734.2.a.k	1
		1734.2.a.l	1
		1734.2.a.m	1
		1734.2.a.n	2
		1734.2.a.o	2
		1734.2.a.p	3
		1734.2.a.q	3
		1734.2.a.r	3
		1734.2.a.s	3
		1734.2.a.t	4
		1734.2.a.u	4
		1734.2.a.v	4
		1734.2.a.w	4
1734.2.b	\(\chi_{1734}(577, \cdot)\)	1734.2.b.a	2	1
		1734.2.b.b	2
		1734.2.b.c	2
		1734.2.b.d	2
		1734.2.b.e	2
		1734.2.b.f	2
		1734.2.b.g	2
		1734.2.b.h	4
		1734.2.b.i	6
		1734.2.b.j	6
		1734.2.b.k	8
		1734.2.b.l	8
1734.2.f	\(\chi_{1734}(829, \cdot)\)	1734.2.f.a	4	2
		1734.2.f.b	4
		1734.2.f.c	4
		1734.2.f.d	4
		1734.2.f.e	4
		1734.2.f.f	4
		1734.2.f.g	4
		1734.2.f.h	4
		1734.2.f.i	4
		1734.2.f.j	8
		1734.2.f.k	8
		1734.2.f.l	8
		1734.2.f.m	8
		1734.2.f.n	12
		1734.2.f.o	12
1734.2.h	\(\chi_{1734}(733, \cdot)\)	n/a	176	4
1734.2.i	\(\chi_{1734}(65, \cdot)\)	n/a	720	8
1734.2.k	\(\chi_{1734}(103, \cdot)\)	n/a	800	16
1734.2.n	\(\chi_{1734}(67, \cdot)\)	n/a	800	16
1734.2.o	\(\chi_{1734}(13, \cdot)\)	n/a	1600	32
1734.2.q	\(\chi_{1734}(19, \cdot)\)	n/a	3328	64
1734.2.t	\(\chi_{1734}(5, \cdot)\)	n/a	13056	128

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1734))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1734)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(867))\)\(^{\oplus 2}\)