Space of modular forms of level 1682 and weight 2

• Label: 1682.2
• Level: 1682
• Weight: 2
• Dimension: 29366
• Nonzero newspaces: 8
• Sturm bound: 353220
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 1682 = 2 \cdot 29^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(353220\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1682))\).

	Total	New	Old
Modular forms	89509	29366	60143
Cusp forms	87102	29366	57736
Eisenstein series	2407	0	2407

Trace form

29366 * q + q^2 + 4 * q^3 + q^4 + 6 * q^5 + 4 * q^6 + 8 * q^7 + q^8 + 13 * q^9 + 6 * q^10 + 12 * q^11 + 4 * q^12 + 14 * q^13 + 8 * q^14 + 24 * q^15 + q^16 + 18 * q^17 + 13 * q^18 + 20 * q^19 - 8 * q^20 - 80 * q^21 - 44 * q^22 - 32 * q^23 - 52 * q^24 - 81 * q^25 - 56 * q^26 - 128 * q^27 + 8 * q^28 - 56 * q^29 - 144 * q^30 - 80 * q^31 + q^32 - 120 * q^33 - 52 * q^34 - 64 * q^35 - 43 * q^36 - 18 * q^37 - 36 * q^38 - 56 * q^39 - 8 * q^40 + 42 * q^41 + 32 * q^42 + 44 * q^43 + 12 * q^44 + 8 * q^45 + 24 * q^46 - 8 * q^47 + 4 * q^48 - 55 * q^49 + 31 * q^50 - 40 * q^51 + 14 * q^52 - 72 * q^53 + 40 * q^54 - 152 * q^55 + 8 * q^56 - 32 * q^57 + 4 * q^59 + 24 * q^60 - 50 * q^61 + 32 * q^62 - 120 * q^63 + q^64 - 42 * q^65 + 48 * q^66 - 44 * q^67 + 18 * q^68 - 16 * q^69 - 8 * q^70 - 152 * q^71 + 13 * q^72 - 108 * q^73 - 130 * q^74 - 156 * q^75 - 92 * q^76 - 184 * q^77 - 168 * q^78 - 32 * q^79 + 6 * q^80 - 327 * q^81 - 70 * q^82 - 140 * q^83 - 136 * q^84 - 228 * q^85 - 236 * q^86 - 140 * q^87 + 12 * q^88 - 190 * q^89 - 202 * q^90 - 224 * q^91 - 144 * q^92 - 96 * q^93 - 64 * q^94 - 328 * q^95 + 4 * q^96 - 28 * q^97 - 167 * q^98 - 236 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1682))\)

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
1682.2.a	\(\chi_{1682}(1, \cdot)\)	1682.2.a.a	1	1
		1682.2.a.b	1
		1682.2.a.c	1
		1682.2.a.d	1
		1682.2.a.e	1
		1682.2.a.f	1
		1682.2.a.g	1
		1682.2.a.h	1
		1682.2.a.i	1
		1682.2.a.j	1
		1682.2.a.k	2
		1682.2.a.l	2
		1682.2.a.m	3
		1682.2.a.n	3
		1682.2.a.o	4
		1682.2.a.p	4
		1682.2.a.q	6
		1682.2.a.r	6
		1682.2.a.s	6
		1682.2.a.t	6
		1682.2.a.u	8
		1682.2.a.v	8
1682.2.b	\(\chi_{1682}(1681, \cdot)\)	1682.2.b.a	2	1
		1682.2.b.b	2
		1682.2.b.c	2
		1682.2.b.d	2
		1682.2.b.e	2
		1682.2.b.f	4
		1682.2.b.g	6
		1682.2.b.h	8
		1682.2.b.i	12
		1682.2.b.j	12
		1682.2.b.k	16
1682.2.d	\(\chi_{1682}(571, \cdot)\)	n/a	402	6
1682.2.e	\(\chi_{1682}(63, \cdot)\)	n/a	408	6
1682.2.g	\(\chi_{1682}(59, \cdot)\)	n/a	2044	28
1682.2.h	\(\chi_{1682}(57, \cdot)\)	n/a	2016	28
1682.2.j	\(\chi_{1682}(7, \cdot)\)	n/a	12264	168
1682.2.k	\(\chi_{1682}(5, \cdot)\)	n/a	12096	168

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1682))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1682)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(841))\)\(^{\oplus 2}\)