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Properties

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

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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

\( 169 q + 3 q^{2} + 3 q^{4} + 2 q^{5} + 3 q^{8} + 3 q^{9} + O(q^{10}) \) \( 169 q + 3 q^{2} + 3 q^{4} + 2 q^{5} + 3 q^{8} + 3 q^{9} + 2 q^{10} + 6 q^{13} + 19 q^{16} + 3 q^{17} - 7 q^{18} - 8 q^{20} - 16 q^{21} + 2 q^{25} - 14 q^{26} + 10 q^{29} - 7 q^{32} - 2 q^{34} + 15 q^{36} - 4 q^{37} + 2 q^{40} + 2 q^{41} + 2 q^{45} - 7 q^{49} + 2 q^{50} + 6 q^{52} + 6 q^{58} - 2 q^{61} + 3 q^{64} - 6 q^{65} - 16 q^{66} - 25 q^{68} - 25 q^{72} + 10 q^{73} - 22 q^{74} + 2 q^{80} - q^{81} - 22 q^{82} - 3 q^{85} - 4 q^{89} - 14 q^{90} + 6 q^{97} - 25 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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