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Properties

Label 277.2
Level 277
Weight 2
Dimension 3060
Nonzero newspaces 8
Newform subspaces 15
Sturm bound 12788
Trace bound 2

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Defining parameters

Level: \( N \) = \( 277 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 15 \)
Sturm bound: \(12788\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(277))\).

Total New Old
Modular forms 3335 3335 0
Cusp forms 3060 3060 0
Eisenstein series 275 275 0

Trace form

\( 3060 q - 135 q^{2} - 134 q^{3} - 131 q^{4} - 132 q^{5} - 126 q^{6} - 130 q^{7} - 123 q^{8} - 125 q^{9} + O(q^{10}) \) \( 3060 q - 135 q^{2} - 134 q^{3} - 131 q^{4} - 132 q^{5} - 126 q^{6} - 130 q^{7} - 123 q^{8} - 125 q^{9} - 120 q^{10} - 126 q^{11} - 110 q^{12} - 124 q^{13} - 114 q^{14} - 114 q^{15} - 107 q^{16} - 120 q^{17} - 99 q^{18} - 118 q^{19} - 96 q^{20} - 106 q^{21} - 102 q^{22} - 114 q^{23} - 78 q^{24} - 107 q^{25} - 96 q^{26} - 98 q^{27} - 82 q^{28} - 108 q^{29} - 66 q^{30} - 106 q^{31} - 75 q^{32} - 90 q^{33} - 84 q^{34} - 90 q^{35} - 47 q^{36} - 100 q^{37} - 78 q^{38} - 82 q^{39} - 48 q^{40} - 96 q^{41} - 42 q^{42} - 94 q^{43} - 54 q^{44} - 60 q^{45} - 66 q^{46} - 90 q^{47} - 14 q^{48} - 81 q^{49} - 45 q^{50} - 66 q^{51} - 40 q^{52} - 84 q^{53} - 18 q^{54} - 66 q^{55} - 18 q^{56} - 58 q^{57} - 48 q^{58} - 78 q^{59} + 30 q^{60} - 76 q^{61} - 42 q^{62} - 34 q^{63} - 11 q^{64} - 54 q^{65} + 6 q^{66} - 70 q^{67} - 12 q^{68} - 42 q^{69} + 6 q^{70} - 66 q^{71} + 57 q^{72} - 64 q^{73} - 24 q^{74} - 14 q^{75} + 2 q^{76} - 42 q^{77} + 30 q^{78} - 58 q^{79} + 48 q^{80} - 17 q^{81} - 12 q^{82} - 54 q^{83} + 86 q^{84} - 30 q^{85} - 6 q^{86} - 18 q^{87} + 42 q^{88} - 48 q^{89} + 96 q^{90} - 26 q^{91} + 30 q^{92} - 10 q^{93} + 6 q^{94} - 18 q^{95} + 114 q^{96} - 40 q^{97} + 33 q^{98} + 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(277))\)

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
277.2.a \(\chi_{277}(1, \cdot)\) 277.2.a.a 1 1
277.2.a.b 3
277.2.a.c 9
277.2.a.d 9
277.2.b \(\chi_{277}(276, \cdot)\) 277.2.b.a 22 1
277.2.c \(\chi_{277}(116, \cdot)\) 277.2.c.a 2 2
277.2.c.b 10
277.2.c.c 32
277.2.e \(\chi_{277}(117, \cdot)\) 277.2.e.a 2 2
277.2.e.b 12
277.2.e.c 32
277.2.g \(\chi_{277}(16, \cdot)\) 277.2.g.a 462 22
277.2.h \(\chi_{277}(4, \cdot)\) 277.2.h.a 484 22
277.2.i \(\chi_{277}(3, \cdot)\) 277.2.i.a 968 44
277.2.k \(\chi_{277}(7, \cdot)\) 277.2.k.a 1012 44