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Properties

Label 309.2
Level 309
Weight 2
Dimension 2549
Nonzero newspaces 8
Newform subspaces 18
Sturm bound 14144
Trace bound 1

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Defining parameters

Level: \( N \) = \( 309 = 3 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 18 \)
Sturm bound: \(14144\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(309))\).

Total New Old
Modular forms 3740 2753 987
Cusp forms 3333 2549 784
Eisenstein series 407 204 203

Trace form

\( 2549 q - 3 q^{2} - 52 q^{3} - 109 q^{4} - 6 q^{5} - 54 q^{6} - 110 q^{7} - 15 q^{8} - 52 q^{9} + O(q^{10}) \) \( 2549 q - 3 q^{2} - 52 q^{3} - 109 q^{4} - 6 q^{5} - 54 q^{6} - 110 q^{7} - 15 q^{8} - 52 q^{9} - 120 q^{10} - 12 q^{11} - 58 q^{12} - 116 q^{13} - 24 q^{14} - 57 q^{15} - 133 q^{16} - 18 q^{17} - 54 q^{18} - 122 q^{19} - 42 q^{20} - 59 q^{21} - 138 q^{22} - 24 q^{23} - 66 q^{24} - 133 q^{25} - 42 q^{26} - 52 q^{27} - 158 q^{28} - 30 q^{29} - 69 q^{30} - 134 q^{31} - 63 q^{32} - 63 q^{33} - 156 q^{34} - 48 q^{35} - 58 q^{36} - 140 q^{37} - 60 q^{38} - 65 q^{39} - 192 q^{40} - 42 q^{41} - 75 q^{42} - 146 q^{43} - 84 q^{44} - 57 q^{45} - 174 q^{46} - 48 q^{47} - 82 q^{48} - 159 q^{49} - 93 q^{50} - 69 q^{51} - 200 q^{52} - 54 q^{53} - 54 q^{54} - 174 q^{55} - 120 q^{56} - 71 q^{57} - 192 q^{58} - 60 q^{59} - 93 q^{60} - 164 q^{61} - 96 q^{62} - 59 q^{63} - 229 q^{64} - 84 q^{65} - 87 q^{66} - 170 q^{67} - 126 q^{68} - 75 q^{69} - 246 q^{70} - 72 q^{71} - 66 q^{72} - 176 q^{73} - 114 q^{74} - 82 q^{75} - 242 q^{76} - 96 q^{77} - 93 q^{78} - 182 q^{79} - 186 q^{80} - 52 q^{81} - 228 q^{82} - 84 q^{83} - 39 q^{84} - 6 q^{85} + 72 q^{86} + 21 q^{87} + 534 q^{88} + 114 q^{89} + 33 q^{90} + 228 q^{91} + 240 q^{92} + 121 q^{93} + 162 q^{94} + 186 q^{95} + 498 q^{96} + 242 q^{97} + 645 q^{98} + 39 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(309))\)

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
309.2.a \(\chi_{309}(1, \cdot)\) 309.2.a.a 1 1
309.2.a.b 3
309.2.a.c 5
309.2.a.d 8
309.2.c \(\chi_{309}(308, \cdot)\) 309.2.c.a 32 1
309.2.e \(\chi_{309}(46, \cdot)\) 309.2.e.a 2 2
309.2.e.b 16
309.2.e.c 16
309.2.g \(\chi_{309}(47, \cdot)\) 309.2.g.a 2 2
309.2.g.b 8
309.2.g.c 56
309.2.i \(\chi_{309}(13, \cdot)\) 309.2.i.a 128 16
309.2.i.b 160
309.2.k \(\chi_{309}(80, \cdot)\) 309.2.k.a 512 16
309.2.m \(\chi_{309}(4, \cdot)\) 309.2.m.a 256 32
309.2.m.b 288
309.2.o \(\chi_{309}(5, \cdot)\) 309.2.o.a 32 32
309.2.o.b 1024

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(309))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(309)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(103))\)\(^{\oplus 2}\)