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Properties

Label 335.2
Level 335
Weight 2
Dimension 3915
Nonzero newspaces 12
Newform subspaces 19
Sturm bound 17952
Trace bound 4

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Defining parameters

Level: \( N \) = \( 335 = 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 19 \)
Sturm bound: \(17952\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(335))\).

Total New Old
Modular forms 4752 4307 445
Cusp forms 4225 3915 310
Eisenstein series 527 392 135

Trace form

\( 3915 q - 69 q^{2} - 70 q^{3} - 73 q^{4} - 100 q^{5} - 210 q^{6} - 74 q^{7} - 81 q^{8} - 79 q^{9} + O(q^{10}) \) \( 3915 q - 69 q^{2} - 70 q^{3} - 73 q^{4} - 100 q^{5} - 210 q^{6} - 74 q^{7} - 81 q^{8} - 79 q^{9} - 102 q^{10} - 210 q^{11} - 94 q^{12} - 80 q^{13} - 90 q^{14} - 103 q^{15} - 229 q^{16} - 84 q^{17} - 105 q^{18} - 86 q^{19} - 106 q^{20} - 230 q^{21} - 102 q^{22} - 90 q^{23} - 126 q^{24} - 100 q^{25} - 240 q^{26} - 106 q^{27} - 122 q^{28} - 96 q^{29} - 111 q^{30} - 230 q^{31} - 129 q^{32} - 114 q^{33} - 120 q^{34} - 107 q^{35} - 289 q^{36} - 104 q^{37} - 126 q^{38} - 122 q^{39} - 114 q^{40} - 240 q^{41} - 162 q^{42} - 110 q^{43} - 150 q^{44} - 112 q^{45} - 270 q^{46} - 114 q^{47} - 190 q^{48} - 123 q^{49} - 102 q^{50} - 270 q^{51} - 76 q^{52} - 54 q^{53} + 12 q^{54} - 12 q^{55} + 78 q^{56} + 8 q^{57} + 108 q^{58} + 6 q^{59} + 137 q^{60} + 4 q^{61} - 30 q^{62} + 116 q^{63} + 467 q^{64} + 19 q^{65} + 252 q^{66} - q^{67} + 6 q^{68} - 30 q^{69} + 141 q^{70} - 6 q^{71} + 399 q^{72} + 146 q^{73} - 48 q^{74} + 29 q^{75} + 190 q^{76} - 30 q^{77} + 30 q^{78} + 8 q^{79} + 68 q^{80} - 121 q^{81} + 6 q^{82} - 84 q^{83} - 202 q^{84} - 117 q^{85} - 330 q^{86} - 186 q^{87} - 246 q^{88} - 156 q^{89} - 138 q^{90} - 310 q^{91} - 234 q^{92} - 194 q^{93} - 210 q^{94} - 119 q^{95} - 450 q^{96} - 164 q^{97} - 237 q^{98} - 222 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(335))\)

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
335.2.a \(\chi_{335}(1, \cdot)\) 335.2.a.a 1 1
335.2.a.b 2
335.2.a.c 2
335.2.a.d 7
335.2.a.e 11
335.2.c \(\chi_{335}(269, \cdot)\) 335.2.c.a 32 1
335.2.e \(\chi_{335}(96, \cdot)\) 335.2.e.a 20 2
335.2.e.b 24
335.2.f \(\chi_{335}(133, \cdot)\) 335.2.f.a 64 2
335.2.i \(\chi_{335}(29, \cdot)\) 335.2.i.a 64 2
335.2.k \(\chi_{335}(76, \cdot)\) 335.2.k.a 110 10
335.2.k.b 130
335.2.m \(\chi_{335}(38, \cdot)\) 335.2.m.a 128 4
335.2.o \(\chi_{335}(9, \cdot)\) 335.2.o.a 320 10
335.2.q \(\chi_{335}(6, \cdot)\) 335.2.q.a 200 20
335.2.q.b 240
335.2.s \(\chi_{335}(3, \cdot)\) 335.2.s.a 640 20
335.2.u \(\chi_{335}(4, \cdot)\) 335.2.u.a 640 20
335.2.w \(\chi_{335}(2, \cdot)\) 335.2.w.a 1280 40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(335))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(335)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 2}\)