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Properties

Label 1980.2.dk
Level $1980$
Weight $2$
Character orbit 1980.dk
Rep. character $\chi_{1980}(103,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $6784$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1980.dk (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1980 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1980, [\chi])\).

Total New Old
Modular forms 7040 7040 0
Cusp forms 6784 6784 0
Eisenstein series 256 256 0

Trace form

\( 6784 q - 6 q^{2} - 12 q^{5} - 24 q^{6} - 24 q^{8} + O(q^{10}) \) \( 6784 q - 6 q^{2} - 12 q^{5} - 24 q^{6} - 24 q^{8} - 64 q^{10} - 44 q^{12} - 12 q^{13} - 12 q^{16} - 48 q^{17} - 4 q^{18} + 26 q^{20} - 128 q^{21} - 12 q^{25} + 16 q^{26} - 56 q^{28} - 32 q^{30} - 16 q^{32} - 20 q^{33} - 40 q^{36} - 48 q^{37} + 2 q^{38} - 6 q^{40} - 24 q^{41} + 12 q^{42} - 24 q^{45} - 48 q^{46} - 6 q^{50} + 26 q^{52} + 24 q^{56} + 24 q^{57} + 10 q^{58} - 88 q^{60} - 24 q^{61} + 172 q^{62} - 32 q^{65} - 4 q^{66} - 22 q^{68} + 34 q^{70} + 14 q^{72} - 48 q^{73} + 40 q^{77} - 88 q^{78} - 304 q^{80} - 48 q^{81} - 40 q^{82} - 12 q^{85} - 12 q^{86} - 120 q^{88} - 116 q^{90} - 34 q^{92} + 48 q^{93} - 140 q^{96} - 12 q^{97} - 104 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1980, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.