↑

Properties

Label 53.2
Level 53
Weight 2
Dimension 92
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 468
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 53 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(468\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(53))\).

Total New Old
Modular forms 143 143 0
Cusp forms 92 92 0
Eisenstein series 51 51 0

Trace form

\( 92 q - 23 q^{2} - 22 q^{3} - 19 q^{4} - 20 q^{5} - 14 q^{6} - 18 q^{7} - 11 q^{8} - 13 q^{9} + O(q^{10}) \) \( 92 q - 23 q^{2} - 22 q^{3} - 19 q^{4} - 20 q^{5} - 14 q^{6} - 18 q^{7} - 11 q^{8} - 13 q^{9} - 8 q^{10} - 14 q^{11} + 2 q^{12} - 12 q^{13} - 2 q^{14} - 2 q^{15} + 5 q^{16} - 8 q^{17} + 13 q^{18} - 6 q^{19} + 16 q^{20} + 6 q^{21} + 10 q^{22} - 2 q^{23} + 34 q^{24} + 5 q^{25} + 16 q^{26} + 14 q^{27} + 30 q^{28} + 4 q^{29} + 46 q^{30} + 6 q^{31} + 37 q^{32} + 22 q^{33} + 28 q^{34} + 22 q^{35} + 65 q^{36} + 12 q^{37} + 34 q^{38} + 30 q^{39} + 25 q^{40} - 10 q^{41} - 34 q^{42} - 34 q^{43} - 46 q^{44} - 78 q^{45} - 6 q^{46} - 4 q^{47} - 162 q^{48} - 21 q^{49} - 50 q^{50} - 58 q^{51} - 110 q^{52} - 51 q^{53} - 88 q^{54} - 32 q^{55} - 62 q^{56} - 50 q^{57} - 53 q^{58} - 18 q^{59} - 118 q^{60} + 10 q^{61} + 18 q^{62} - 52 q^{63} - 3 q^{64} + 6 q^{65} + 14 q^{66} + 16 q^{67} + 61 q^{68} + 70 q^{69} + 118 q^{70} + 46 q^{71} + 169 q^{72} + 48 q^{73} + 88 q^{74} + 98 q^{75} + 114 q^{76} + 70 q^{77} + 142 q^{78} + 54 q^{79} + 160 q^{80} + 95 q^{81} + 100 q^{82} + 58 q^{83} + 198 q^{84} + 82 q^{85} + 106 q^{86} + 42 q^{87} + 24 q^{88} - q^{89} - 18 q^{91} - 92 q^{92} - 2 q^{93} - 194 q^{94} - 10 q^{95} - 34 q^{96} - 149 q^{97} - 63 q^{98} - 130 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)

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
53.2.a \(\chi_{53}(1, \cdot)\) 53.2.a.a 1 1
53.2.a.b 3
53.2.b \(\chi_{53}(52, \cdot)\) 53.2.b.a 4 1
53.2.d \(\chi_{53}(10, \cdot)\) 53.2.d.a 36 12
53.2.e \(\chi_{53}(4, \cdot)\) 53.2.e.a 48 12