Space of modular forms of level 1700 and weight 1

• Label: 1700.1
• Level: 1700
• Weight: 1
• Dimension: 169
• Nonzero newspaces: 12
• Newform subspaces: 26
• Sturm bound: 172800
• Trace bound: 53

Defining parameters

Level:	\( N \)	=	\( 1700 = 2^{2} \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 26 \)
Sturm bound:			\(172800\)
Trace bound:			\(53\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1700))\).

	Total	New	Old
Modular forms	2474	783	1691
Cusp forms	234	169	65
Eisenstein series	2240	614	1626

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	169	0	0	0

Trace form

169 * q + 3 * q^2 + 3 * q^4 + 2 * q^5 + 3 * q^8 + 3 * q^9 + 2 * q^10 + 6 * q^13 + 19 * q^16 + 3 * q^17 - 7 * q^18 - 8 * q^20 - 16 * q^21 + 2 * q^25 - 14 * q^26 + 10 * q^29 - 7 * q^32 - 2 * q^34 + 15 * q^36 - 4 * q^37 + 2 * q^40 + 2 * q^41 + 2 * q^45 - 7 * q^49 + 2 * q^50 + 6 * q^52 + 6 * q^58 - 2 * q^61 + 3 * q^64 - 6 * q^65 - 16 * q^66 - 25 * q^68 - 25 * q^72 + 10 * q^73 - 22 * q^74 + 2 * q^80 - q^81 - 22 * q^82 - 3 * q^85 - 4 * q^89 - 14 * q^90 + 6 * q^97 - 25 * q^98

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1700))\)

We only show spaces with odd 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
1700.1.b	\(\chi_{1700}(851, \cdot)\)	None	0	1
1700.1.d	\(\chi_{1700}(1699, \cdot)\)	1700.1.d.a	2	1
		1700.1.d.b	2
		1700.1.d.c	2
		1700.1.d.d	4
1700.1.f	\(\chi_{1700}(1599, \cdot)\)	None	0	1
1700.1.h	\(\chi_{1700}(951, \cdot)\)	1700.1.h.a	1	1
		1700.1.h.b	1
		1700.1.h.c	1
		1700.1.h.d	1
		1700.1.h.e	1
		1700.1.h.f	2
		1700.1.h.g	2
1700.1.j	\(\chi_{1700}(157, \cdot)\)	None	0	2
1700.1.k	\(\chi_{1700}(1257, \cdot)\)	None	0	2
1700.1.n	\(\chi_{1700}(599, \cdot)\)	1700.1.n.a	2	2
		1700.1.n.b	2
1700.1.p	\(\chi_{1700}(251, \cdot)\)	1700.1.p.a	2	2
1700.1.q	\(\chi_{1700}(1157, \cdot)\)	None	0	2
1700.1.t	\(\chi_{1700}(293, \cdot)\)	None	0	2
1700.1.w	\(\chi_{1700}(151, \cdot)\)	1700.1.w.a	4	4
		1700.1.w.b	4
1700.1.y	\(\chi_{1700}(93, \cdot)\)	None	0	4
1700.1.z	\(\chi_{1700}(393, \cdot)\)	None	0	4
1700.1.bb	\(\chi_{1700}(399, \cdot)\)	None	0	4
1700.1.bd	\(\chi_{1700}(271, \cdot)\)	1700.1.bd.a	4	4
		1700.1.bd.b	4
1700.1.bf	\(\chi_{1700}(239, \cdot)\)	None	0	4
1700.1.bh	\(\chi_{1700}(339, \cdot)\)	None	0	4
1700.1.bj	\(\chi_{1700}(171, \cdot)\)	None	0	4
1700.1.bk	\(\chi_{1700}(7, \cdot)\)	1700.1.bk.a	8	8
1700.1.bm	\(\chi_{1700}(201, \cdot)\)	None	0	8
1700.1.bp	\(\chi_{1700}(249, \cdot)\)	None	0	8
1700.1.br	\(\chi_{1700}(107, \cdot)\)	1700.1.br.a	8	8
1700.1.bs	\(\chi_{1700}(217, \cdot)\)	None	0	8
1700.1.bv	\(\chi_{1700}(137, \cdot)\)	None	0	8
1700.1.bw	\(\chi_{1700}(191, \cdot)\)	1700.1.bw.a	8	8
		1700.1.bw.b	8
1700.1.by	\(\chi_{1700}(259, \cdot)\)	None	0	8
1700.1.cb	\(\chi_{1700}(33, \cdot)\)	None	0	8
1700.1.cc	\(\chi_{1700}(13, \cdot)\)	None	0	8
1700.1.cf	\(\chi_{1700}(19, \cdot)\)	1700.1.cf.a	16	16
		1700.1.cf.b	16
1700.1.cg	\(\chi_{1700}(117, \cdot)\)	None	0	16
1700.1.cj	\(\chi_{1700}(53, \cdot)\)	None	0	16
1700.1.ck	\(\chi_{1700}(111, \cdot)\)	None	0	16
1700.1.cm	\(\chi_{1700}(23, \cdot)\)	1700.1.cm.a	32	32
1700.1.co	\(\chi_{1700}(29, \cdot)\)	None	0	32
1700.1.cr	\(\chi_{1700}(41, \cdot)\)	None	0	32
1700.1.ct	\(\chi_{1700}(3, \cdot)\)	1700.1.ct.a	32	32

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1700))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1700)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(340))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(850))\)\(^{\oplus 2}\)