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Properties

Label 268.2
Level 268
Weight 2
Dimension 1243
Nonzero newspaces 8
Newform subspaces 10
Sturm bound 8976
Trace bound 1

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Defining parameters

Level: \( N \) = \( 268 = 2^{2} \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 10 \)
Sturm bound: \(8976\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(268))\).

Total New Old
Modular forms 2409 1375 1034
Cusp forms 2080 1243 837
Eisenstein series 329 132 197

Trace form

\( 1243 q - 33 q^{2} - 33 q^{4} - 66 q^{5} - 33 q^{6} - 33 q^{8} - 66 q^{9} + O(q^{10}) \) \( 1243 q - 33 q^{2} - 33 q^{4} - 66 q^{5} - 33 q^{6} - 33 q^{8} - 66 q^{9} - 33 q^{10} - 33 q^{12} - 66 q^{13} - 33 q^{14} - 33 q^{16} - 66 q^{17} - 33 q^{18} - 33 q^{20} - 66 q^{21} - 33 q^{22} - 33 q^{24} - 66 q^{25} - 33 q^{26} - 33 q^{28} - 66 q^{29} - 33 q^{30} - 33 q^{32} - 66 q^{33} - 33 q^{34} - 33 q^{36} - 66 q^{37} - 33 q^{38} - 33 q^{40} - 66 q^{41} - 33 q^{42} - 33 q^{44} - 66 q^{45} - 33 q^{46} - 33 q^{48} - 66 q^{49} - 33 q^{50} - 33 q^{52} - 99 q^{53} - 33 q^{54} - 99 q^{55} - 33 q^{56} - 143 q^{57} - 33 q^{58} - 66 q^{59} - 33 q^{60} - 198 q^{61} - 33 q^{62} - 143 q^{63} - 33 q^{64} - 198 q^{65} - 66 q^{67} - 66 q^{68} - 132 q^{69} - 33 q^{70} - 132 q^{71} - 33 q^{72} - 209 q^{73} - 33 q^{74} - 132 q^{75} - 33 q^{76} - 132 q^{77} - 33 q^{78} - 77 q^{79} - 33 q^{80} - 165 q^{81} - 33 q^{82} - 33 q^{83} - 33 q^{84} - 66 q^{85} - 33 q^{86} - 33 q^{88} - 66 q^{89} - 33 q^{90} - 33 q^{92} - 66 q^{93} - 33 q^{94} - 33 q^{96} - 66 q^{97} - 33 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(268))\)

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
268.2.a \(\chi_{268}(1, \cdot)\) 268.2.a.a 1 1
268.2.a.b 2
268.2.a.c 2
268.2.d \(\chi_{268}(267, \cdot)\) 268.2.d.a 32 1
268.2.e \(\chi_{268}(29, \cdot)\) 268.2.e.a 12 2
268.2.h \(\chi_{268}(231, \cdot)\) 268.2.h.a 64 2
268.2.i \(\chi_{268}(9, \cdot)\) 268.2.i.a 50 10
268.2.j \(\chi_{268}(3, \cdot)\) 268.2.j.a 320 10
268.2.m \(\chi_{268}(17, \cdot)\) 268.2.m.a 120 20
268.2.n \(\chi_{268}(7, \cdot)\) 268.2.n.a 640 20

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(268))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(268)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(134))\)\(^{\oplus 2}\)