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Properties

Label 51.2
Level 51
Weight 2
Dimension 55
Nonzero newspaces 5
Newform subspaces 7
Sturm bound 384
Trace bound 4

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Defining parameters

Level: \( N \) = \( 51 = 3 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 7 \)
Sturm bound: \(384\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(51))\).

Total New Old
Modular forms 128 87 41
Cusp forms 65 55 10
Eisenstein series 63 32 31

Trace form

\( 55 q - 3 q^{2} - 9 q^{3} - 23 q^{4} - 6 q^{5} - 11 q^{6} - 24 q^{7} - 15 q^{8} - 9 q^{9} + O(q^{10}) \) \( 55 q - 3 q^{2} - 9 q^{3} - 23 q^{4} - 6 q^{5} - 11 q^{6} - 24 q^{7} - 15 q^{8} - 9 q^{9} - 26 q^{10} + 4 q^{11} + 9 q^{12} - 14 q^{13} + 8 q^{14} + 10 q^{15} + 25 q^{16} - q^{17} + 13 q^{18} - 20 q^{19} + 14 q^{20} + 8 q^{21} - 20 q^{22} - 8 q^{23} + 17 q^{24} + 9 q^{25} + 30 q^{26} - 9 q^{27} + 24 q^{28} + 10 q^{29} + 38 q^{30} + 16 q^{31} + 17 q^{32} + 20 q^{33} + 61 q^{34} + 16 q^{35} + 17 q^{36} + 10 q^{37} + 20 q^{38} - 6 q^{39} + 22 q^{40} - 2 q^{41} - 32 q^{42} - 12 q^{43} - 20 q^{44} - 38 q^{45} - 56 q^{46} - 48 q^{47} - 95 q^{48} - 73 q^{49} - 93 q^{50} - 57 q^{51} - 130 q^{52} - 30 q^{53} - 27 q^{54} - 24 q^{55} - 40 q^{56} - 12 q^{57} + 6 q^{58} + 4 q^{59} - 10 q^{60} + 18 q^{61} + 16 q^{62} + 56 q^{63} + 17 q^{64} + 36 q^{65} + 36 q^{66} - 4 q^{67} + 81 q^{68} + 72 q^{69} + 112 q^{70} + 24 q^{71} + 73 q^{72} + 110 q^{73} + 54 q^{74} + 89 q^{75} + 84 q^{76} + 64 q^{77} + 118 q^{78} + 32 q^{79} + 86 q^{80} + 47 q^{81} + 74 q^{82} + 28 q^{83} + 40 q^{84} + 2 q^{85} - 68 q^{86} - 38 q^{87} - 4 q^{88} - 42 q^{89} - 98 q^{90} - 32 q^{91} - 8 q^{92} - 72 q^{93} - 32 q^{94} - 56 q^{95} - 111 q^{96} - 50 q^{97} - 99 q^{98} - 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)

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
51.2.a \(\chi_{51}(1, \cdot)\) 51.2.a.a 1 1
51.2.a.b 2
51.2.d \(\chi_{51}(16, \cdot)\) 51.2.d.a 2 1
51.2.d.b 2
51.2.e \(\chi_{51}(4, \cdot)\) 51.2.e.a 8 2
51.2.h \(\chi_{51}(19, \cdot)\) 51.2.h.a 8 4
51.2.i \(\chi_{51}(5, \cdot)\) 51.2.i.a 32 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(51))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(51)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)