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Properties

Label 229.2
Level 229
Weight 2
Dimension 2072
Nonzero newspaces 8
Newform subspaces 12
Sturm bound 8740
Trace bound 3

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Defining parameters

Level: \( N \) = \( 229 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 12 \)
Sturm bound: \(8740\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(229))\).

Total New Old
Modular forms 2299 2299 0
Cusp forms 2072 2072 0
Eisenstein series 227 227 0

Trace form

\( 2072 q - 111 q^{2} - 110 q^{3} - 107 q^{4} - 108 q^{5} - 102 q^{6} - 106 q^{7} - 99 q^{8} - 101 q^{9} + O(q^{10}) \) \( 2072 q - 111 q^{2} - 110 q^{3} - 107 q^{4} - 108 q^{5} - 102 q^{6} - 106 q^{7} - 99 q^{8} - 101 q^{9} - 96 q^{10} - 102 q^{11} - 86 q^{12} - 100 q^{13} - 90 q^{14} - 90 q^{15} - 83 q^{16} - 96 q^{17} - 75 q^{18} - 94 q^{19} - 72 q^{20} - 82 q^{21} - 78 q^{22} - 90 q^{23} - 54 q^{24} - 83 q^{25} - 72 q^{26} - 74 q^{27} - 58 q^{28} - 84 q^{29} - 42 q^{30} - 82 q^{31} - 51 q^{32} - 66 q^{33} - 60 q^{34} - 66 q^{35} - 23 q^{36} - 76 q^{37} - 54 q^{38} - 58 q^{39} - 24 q^{40} - 72 q^{41} - 18 q^{42} - 70 q^{43} - 30 q^{44} - 36 q^{45} - 42 q^{46} - 66 q^{47} + 10 q^{48} - 57 q^{49} - 21 q^{50} - 42 q^{51} - 16 q^{52} - 60 q^{53} + 6 q^{54} - 42 q^{55} + 6 q^{56} - 34 q^{57} - 24 q^{58} - 54 q^{59} + 54 q^{60} - 52 q^{61} - 18 q^{62} - 10 q^{63} + 13 q^{64} - 30 q^{65} + 30 q^{66} - 46 q^{67} + 12 q^{68} - 18 q^{69} + 30 q^{70} - 42 q^{71} + 81 q^{72} - 40 q^{73} + 10 q^{75} + 26 q^{76} - 18 q^{77} + 54 q^{78} - 34 q^{79} + 72 q^{80} + 7 q^{81} + 12 q^{82} - 30 q^{83} + 110 q^{84} - 6 q^{85} + 18 q^{86} + 6 q^{87} + 66 q^{88} - 24 q^{89} + 120 q^{90} - 2 q^{91} + 54 q^{92} + 14 q^{93} + 30 q^{94} + 6 q^{95} + 138 q^{96} - 16 q^{97} + 57 q^{98} + 42 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(229))\)

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
229.2.a \(\chi_{229}(1, \cdot)\) 229.2.a.a 1 1
229.2.a.b 6
229.2.a.c 11
229.2.b \(\chi_{229}(228, \cdot)\) 229.2.b.a 2 1
229.2.b.b 16
229.2.c \(\chi_{229}(94, \cdot)\) 229.2.c.a 36 2
229.2.e \(\chi_{229}(95, \cdot)\) 229.2.e.a 2 2
229.2.e.b 36
229.2.g \(\chi_{229}(16, \cdot)\) 229.2.g.a 306 18
229.2.h \(\chi_{229}(4, \cdot)\) 229.2.h.a 324 18
229.2.i \(\chi_{229}(3, \cdot)\) 229.2.i.a 648 36
229.2.k \(\chi_{229}(5, \cdot)\) 229.2.k.a 684 36