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Properties

Label 1980.2.df
Level $1980$
Weight $2$
Character orbit 1980.df
Rep. character $\chi_{1980}(151,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $2304$
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.df (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 396 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 3520 2304 1216
Cusp forms 3392 2304 1088
Eisenstein series 128 0 128

Trace form

\( 2304 q - 8 q^{9} + O(q^{10}) \) \( 2304 q - 8 q^{9} + 288 q^{25} - 32 q^{26} + 56 q^{33} + 16 q^{36} + 20 q^{38} - 46 q^{42} - 76 q^{44} + 112 q^{48} + 288 q^{49} + 188 q^{56} - 40 q^{57} + 42 q^{60} + 74 q^{66} - 130 q^{68} + 64 q^{69} + 140 q^{74} + 16 q^{77} - 24 q^{78} + 48 q^{80} + 40 q^{81} - 104 q^{86} - 32 q^{89} - 20 q^{92} + 32 q^{93} + 70 q^{96} + 36 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1980, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 2}\)