↑

Properties

Label 1670.2
Level 1670
Weight 2
Dimension 25565
Nonzero newspaces 6
Sturm bound 334656
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 1670 = 2 \cdot 5 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(334656\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1670))\).

Total New Old
Modular forms 84992 25565 59427
Cusp forms 82337 25565 56772
Eisenstein series 2655 0 2655

Trace form

\( 25565 q + q^{2} + 4 q^{3} + q^{4} + q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} + O(q^{10}) \) \( 25565 q + q^{2} + 4 q^{3} + q^{4} + q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} + q^{10} + 12 q^{11} + 4 q^{12} + 14 q^{13} + 8 q^{14} + 4 q^{15} + q^{16} + 18 q^{17} + 13 q^{18} + 20 q^{19} + q^{20} + 32 q^{21} + 12 q^{22} + 24 q^{23} + 4 q^{24} + q^{25} + 14 q^{26} + 40 q^{27} + 8 q^{28} + 30 q^{29} + 4 q^{30} + 32 q^{31} + q^{32} + 48 q^{33} + 18 q^{34} + 8 q^{35} + 13 q^{36} + 38 q^{37} + 20 q^{38} + 56 q^{39} + q^{40} + 42 q^{41} + 32 q^{42} + 44 q^{43} + 12 q^{44} + 13 q^{45} + 24 q^{46} + 48 q^{47} + 4 q^{48} + 57 q^{49} + q^{50} + 72 q^{51} + 14 q^{52} + 54 q^{53} + 40 q^{54} + 12 q^{55} + 8 q^{56} + 80 q^{57} + 30 q^{58} + 60 q^{59} + 4 q^{60} + 62 q^{61} + 32 q^{62} + 104 q^{63} + q^{64} + 14 q^{65} + 48 q^{66} + 68 q^{67} + 18 q^{68} + 96 q^{69} + 8 q^{70} + 72 q^{71} + 13 q^{72} + 74 q^{73} + 38 q^{74} + 4 q^{75} + 20 q^{76} + 96 q^{77} + 56 q^{78} + 80 q^{79} + q^{80} + 121 q^{81} + 42 q^{82} + 84 q^{83} + 32 q^{84} + 18 q^{85} + 44 q^{86} + 120 q^{87} + 12 q^{88} + 90 q^{89} + 13 q^{90} + 112 q^{91} + 24 q^{92} + 128 q^{93} + 48 q^{94} + 20 q^{95} + 4 q^{96} + 98 q^{97} + 57 q^{98} + 156 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1670))\)

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
1670.2.a \(\chi_{1670}(1, \cdot)\) 1670.2.a.a 1 1
1670.2.a.b 1
1670.2.a.c 5
1670.2.a.d 5
1670.2.a.e 5
1670.2.a.f 6
1670.2.a.g 8
1670.2.a.h 8
1670.2.a.i 9
1670.2.a.j 9
1670.2.b \(\chi_{1670}(669, \cdot)\) 1670.2.b.a 2 1
1670.2.b.b 36
1670.2.b.c 46
1670.2.f \(\chi_{1670}(333, \cdot)\) n/a 168 2
1670.2.g \(\chi_{1670}(11, \cdot)\) n/a 4592 82
1670.2.j \(\chi_{1670}(9, \cdot)\) n/a 6888 82
1670.2.k \(\chi_{1670}(13, \cdot)\) n/a 13776 164

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1670))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1670)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(835))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1670))\)\(^{\oplus 1}\)