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Properties

Label 127.2
Level 127
Weight 2
Dimension 610
Nonzero newspaces 6
Newform subspaces 7
Sturm bound 2688
Trace bound 1

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Defining parameters

Level: \( N \) = \( 127 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 7 \)
Sturm bound: \(2688\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(127))\).

Total New Old
Modular forms 735 735 0
Cusp forms 610 610 0
Eisenstein series 125 125 0

Trace form

\( 610 q - 60 q^{2} - 59 q^{3} - 56 q^{4} - 57 q^{5} - 51 q^{6} - 55 q^{7} - 48 q^{8} - 50 q^{9} + O(q^{10}) \) \( 610 q - 60 q^{2} - 59 q^{3} - 56 q^{4} - 57 q^{5} - 51 q^{6} - 55 q^{7} - 48 q^{8} - 50 q^{9} - 45 q^{10} - 51 q^{11} - 35 q^{12} - 49 q^{13} - 39 q^{14} - 39 q^{15} - 32 q^{16} - 45 q^{17} - 24 q^{18} - 43 q^{19} - 21 q^{20} - 31 q^{21} - 27 q^{22} - 39 q^{23} - 3 q^{24} - 32 q^{25} - 21 q^{26} - 23 q^{27} - 7 q^{28} - 33 q^{29} + 9 q^{30} - 31 q^{31} - 15 q^{33} - 9 q^{34} - 15 q^{35} + 28 q^{36} - 25 q^{37} - 3 q^{38} - 7 q^{39} + 27 q^{40} - 21 q^{41} + 33 q^{42} - 19 q^{43} + 21 q^{44} + 15 q^{45} + 9 q^{46} - 15 q^{47} + 61 q^{48} - 6 q^{49} + 30 q^{50} + 9 q^{51} + 35 q^{52} - 9 q^{53} + 57 q^{54} + 9 q^{55} + 57 q^{56} + 17 q^{57} + 27 q^{58} - 3 q^{59} + 105 q^{60} - q^{61} + 33 q^{62} + 41 q^{63} + 64 q^{64} + 21 q^{65} + 81 q^{66} + 5 q^{67} + 63 q^{68} + 33 q^{69} + 81 q^{70} + 9 q^{71} + 132 q^{72} + 11 q^{73} + 51 q^{74} + 61 q^{75} + 77 q^{76} + 33 q^{77} + 105 q^{78} + 17 q^{79} + 123 q^{80} + 58 q^{81} + 63 q^{82} + 21 q^{83} + 161 q^{84} + 45 q^{85} + 69 q^{86} + 57 q^{87} + 117 q^{88} + 27 q^{89} + 171 q^{90} + 49 q^{91} + 105 q^{92} + 65 q^{93} + 81 q^{94} + 57 q^{95} + 189 q^{96} + 35 q^{97} + 108 q^{98} + 93 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(127))\)

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
127.2.a \(\chi_{127}(1, \cdot)\) 127.2.a.a 3 1
127.2.a.b 7
127.2.c \(\chi_{127}(19, \cdot)\) 127.2.c.a 18 2
127.2.e \(\chi_{127}(2, \cdot)\) 127.2.e.a 54 6
127.2.f \(\chi_{127}(22, \cdot)\) 127.2.f.a 60 6
127.2.i \(\chi_{127}(25, \cdot)\) 127.2.i.a 108 12
127.2.k \(\chi_{127}(9, \cdot)\) 127.2.k.a 360 36