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Properties

Label 1960.2.dm
Level $1960$
Weight $2$
Character orbit 1960.dm
Rep. character $\chi_{1960}(157,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $7968$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.dm (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1960 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1960, [\chi])\).

Total New Old
Modular forms 8160 8160 0
Cusp forms 7968 7968 0
Eisenstein series 192 192 0

Trace form

\( 7968 q - 26 q^{2} - 56 q^{6} - 48 q^{7} - 32 q^{8} + O(q^{10}) \) \( 7968 q - 26 q^{2} - 56 q^{6} - 48 q^{7} - 32 q^{8} - 22 q^{10} - 22 q^{12} - 40 q^{15} - 44 q^{16} - 44 q^{17} + 2 q^{18} - 28 q^{20} - 12 q^{22} - 52 q^{23} - 52 q^{25} - 44 q^{26} + 22 q^{28} - 2 q^{30} - 144 q^{31} - 26 q^{32} - 44 q^{33} - 8 q^{36} - 32 q^{38} - 82 q^{40} - 112 q^{41} - 18 q^{42} - 52 q^{46} + 28 q^{47} + 168 q^{50} - 100 q^{52} - 56 q^{55} - 36 q^{56} - 100 q^{57} - 6 q^{58} - 54 q^{60} - 56 q^{62} - 32 q^{63} - 52 q^{65} + 296 q^{66} - 102 q^{68} - 56 q^{70} + 80 q^{71} - 270 q^{72} - 44 q^{73} - 168 q^{76} - 52 q^{78} - 90 q^{80} - 576 q^{81} - 114 q^{82} - 8 q^{86} - 8 q^{87} + 244 q^{88} - 28 q^{90} - 40 q^{92} - 176 q^{95} + 292 q^{96} - 332 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1960, [\chi])\) into newform subspaces

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