↑

Properties

Label 85.2
Level 85
Weight 2
Dimension 215
Nonzero newspaces 10
Newform subspaces 14
Sturm bound 1152
Trace bound 8

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 85 = 5 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 14 \)
Sturm bound: \(1152\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(85))\).

Total New Old
Modular forms 352 307 45
Cusp forms 225 215 10
Eisenstein series 127 92 35

Trace form

\( 215 q - 19 q^{2} - 20 q^{3} - 23 q^{4} - 25 q^{5} - 60 q^{6} - 24 q^{7} - 31 q^{8} - 29 q^{9} + O(q^{10}) \) \( 215 q - 19 q^{2} - 20 q^{3} - 23 q^{4} - 25 q^{5} - 60 q^{6} - 24 q^{7} - 31 q^{8} - 29 q^{9} - 23 q^{10} - 44 q^{11} + 4 q^{12} - 14 q^{13} - 8 q^{14} - 4 q^{15} - 7 q^{16} - 17 q^{17} - 7 q^{18} - 20 q^{19} - 3 q^{20} - 32 q^{21} - 20 q^{22} - 24 q^{23} + 4 q^{24} + 3 q^{25} - 18 q^{26} - 8 q^{27} + 24 q^{28} - 6 q^{29} + 28 q^{30} - 16 q^{31} + 33 q^{32} + 16 q^{33} + 61 q^{34} - 24 q^{35} + 21 q^{36} + 10 q^{37} + 20 q^{38} + 24 q^{39} + 57 q^{40} - 2 q^{41} + 80 q^{42} + 20 q^{43} + 92 q^{44} + 15 q^{45} - 24 q^{46} + 16 q^{47} + 68 q^{48} - 9 q^{49} - 3 q^{50} - 52 q^{51} - 2 q^{52} + 18 q^{53} + 104 q^{54} + 28 q^{55} + 72 q^{56} + 96 q^{57} + 70 q^{58} + 52 q^{59} + 116 q^{60} + 18 q^{61} + 96 q^{62} + 120 q^{63} - 47 q^{64} + 38 q^{65} + 64 q^{66} - 4 q^{67} + 17 q^{68} + 32 q^{69} - 40 q^{70} - 88 q^{71} - 59 q^{72} - 50 q^{73} - 106 q^{74} - 28 q^{75} - 204 q^{76} - 80 q^{77} - 104 q^{78} - 96 q^{79} - 199 q^{80} - 153 q^{81} - 198 q^{82} - 68 q^{83} - 288 q^{84} - 141 q^{85} - 132 q^{86} - 136 q^{87} - 260 q^{88} - 58 q^{89} - 107 q^{90} - 128 q^{91} - 120 q^{92} - 80 q^{93} - 96 q^{94} - 60 q^{95} - 28 q^{96} - 114 q^{97} + 13 q^{98} - 28 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)

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
85.2.a \(\chi_{85}(1, \cdot)\) 85.2.a.a 1 1
85.2.a.b 2
85.2.a.c 2
85.2.b \(\chi_{85}(69, \cdot)\) 85.2.b.a 8 1
85.2.c \(\chi_{85}(84, \cdot)\) 85.2.c.a 8 1
85.2.d \(\chi_{85}(16, \cdot)\) 85.2.d.a 6 1
85.2.e \(\chi_{85}(21, \cdot)\) 85.2.e.a 12 2
85.2.j \(\chi_{85}(4, \cdot)\) 85.2.j.a 2 2
85.2.j.b 2
85.2.j.c 12
85.2.l \(\chi_{85}(26, \cdot)\) 85.2.l.a 24 4
85.2.m \(\chi_{85}(9, \cdot)\) 85.2.m.a 24 4
85.2.o \(\chi_{85}(3, \cdot)\) 85.2.o.a 56 8
85.2.r \(\chi_{85}(12, \cdot)\) 85.2.r.a 56 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(85))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(85)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)