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Properties

Label 1980.2.bh
Level $1980$
Weight $2$
Character orbit 1980.bh
Rep. character $\chi_{1980}(551,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $480$
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.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 880 480 400
Cusp forms 848 480 368
Eisenstein series 32 0 32

Trace form

\( 480 q - 12 q^{6} + O(q^{10}) \) \( 480 q - 12 q^{6} + 44 q^{12} + 60 q^{14} + 32 q^{18} + 8 q^{21} + 40 q^{24} + 240 q^{25} + 24 q^{29} + 12 q^{34} - 28 q^{36} - 60 q^{38} + 12 q^{40} + 60 q^{42} + 16 q^{45} + 24 q^{46} - 44 q^{48} + 240 q^{49} + 36 q^{52} - 20 q^{54} + 36 q^{58} + 96 q^{64} - 20 q^{66} + 60 q^{68} - 8 q^{69} - 112 q^{72} - 168 q^{74} - 12 q^{76} + 48 q^{78} - 40 q^{81} + 72 q^{82} - 40 q^{84} + 108 q^{86} + 36 q^{90} - 60 q^{92} + 96 q^{93} - 36 q^{94} + 128 q^{96} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1980, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1980, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)