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Properties

Label 255.2
Level 255
Weight 2
Dimension 1487
Nonzero newspaces 18
Newform subspaces 31
Sturm bound 9216
Trace bound 10

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Defining parameters

Level: \( N \) = \( 255 = 3 \cdot 5 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Newform subspaces: \( 31 \)
Sturm bound: \(9216\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(255))\).

Total New Old
Modular forms 2560 1663 897
Cusp forms 2049 1487 562
Eisenstein series 511 176 335

Trace form

\( 1487 q + 5 q^{2} - 13 q^{3} - 23 q^{4} - q^{5} - 47 q^{6} - 24 q^{7} + 9 q^{8} - 17 q^{9} + O(q^{10}) \) \( 1487 q + 5 q^{2} - 13 q^{3} - 23 q^{4} - q^{5} - 47 q^{6} - 24 q^{7} + 9 q^{8} - 17 q^{9} - 51 q^{10} - 12 q^{11} - 59 q^{12} - 46 q^{13} - 40 q^{14} - 45 q^{15} - 207 q^{16} - 17 q^{17} - 91 q^{18} - 52 q^{19} - 47 q^{20} - 88 q^{21} - 68 q^{22} - 8 q^{23} - 75 q^{24} - 105 q^{25} - 106 q^{26} - 13 q^{27} - 168 q^{28} - 46 q^{29} - 87 q^{30} - 192 q^{31} - 87 q^{32} - 92 q^{33} - 235 q^{34} - 56 q^{35} - 103 q^{36} - 102 q^{37} - 92 q^{38} - 38 q^{39} - 167 q^{40} - 58 q^{41} + 8 q^{42} - 92 q^{43} - 52 q^{44} - q^{45} - 88 q^{46} + 32 q^{47} + 125 q^{48} + 39 q^{49} + 5 q^{50} + 35 q^{51} + 30 q^{52} + 26 q^{53} + 17 q^{54} - 92 q^{55} - 40 q^{56} - 20 q^{57} - 170 q^{58} - 60 q^{59} - 59 q^{60} - 222 q^{61} - 128 q^{62} - 152 q^{63} + 17 q^{64} - 102 q^{65} - 164 q^{66} - 148 q^{67} - 183 q^{68} - 168 q^{69} - 40 q^{70} + 24 q^{71} - 103 q^{72} - 58 q^{73} + 46 q^{74} - 21 q^{75} + 84 q^{76} + 32 q^{77} - 50 q^{78} + 48 q^{79} + 401 q^{80} - 161 q^{81} + 226 q^{82} + 28 q^{83} + 248 q^{84} + 231 q^{85} + 268 q^{86} + 202 q^{87} + 556 q^{88} + 198 q^{89} + 85 q^{90} + 208 q^{91} + 488 q^{92} + 208 q^{93} + 384 q^{94} + 204 q^{95} + 341 q^{96} + 190 q^{97} + 301 q^{98} + 148 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(255))\)

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
255.2.a \(\chi_{255}(1, \cdot)\) 255.2.a.a 2 1
255.2.a.b 2
255.2.a.c 3
255.2.a.d 4
255.2.b \(\chi_{255}(154, \cdot)\) 255.2.b.a 2 1
255.2.b.b 4
255.2.b.c 10
255.2.d \(\chi_{255}(169, \cdot)\) 255.2.d.a 8 1
255.2.d.b 8
255.2.g \(\chi_{255}(16, \cdot)\) 255.2.g.a 4 1
255.2.g.b 8
255.2.j \(\chi_{255}(106, \cdot)\) 255.2.j.a 8 2
255.2.j.b 16
255.2.k \(\chi_{255}(98, \cdot)\) 255.2.k.a 8 2
255.2.k.b 56
255.2.m \(\chi_{255}(137, \cdot)\) 255.2.m.a 64 2
255.2.o \(\chi_{255}(152, \cdot)\) 255.2.o.a 8 2
255.2.o.b 56
255.2.r \(\chi_{255}(38, \cdot)\) 255.2.r.a 8 2
255.2.r.b 56
255.2.s \(\chi_{255}(4, \cdot)\) 255.2.s.a 32 2
255.2.v \(\chi_{255}(53, \cdot)\) 255.2.v.a 128 4
255.2.w \(\chi_{255}(76, \cdot)\) 255.2.w.a 16 4
255.2.w.b 32
255.2.z \(\chi_{255}(19, \cdot)\) 255.2.z.a 80 4
255.2.ba \(\chi_{255}(2, \cdot)\) 255.2.ba.a 128 4
255.2.bd \(\chi_{255}(7, \cdot)\) 255.2.bd.a 144 8
255.2.be \(\chi_{255}(14, \cdot)\) 255.2.be.a 32 8
255.2.be.b 224
255.2.bg \(\chi_{255}(11, \cdot)\) 255.2.bg.a 192 8
255.2.bi \(\chi_{255}(22, \cdot)\) 255.2.bi.a 144 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(255))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(255)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 2}\)