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Properties

Label 1980.2.be
Level $1980$
Weight $2$
Character orbit 1980.be
Rep. character $\chi_{1980}(571,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $576$
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.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 396 \)
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 880 576 304
Cusp forms 848 576 272
Eisenstein series 32 0 32

Trace form

\( 576 q + 8 q^{9} + O(q^{10}) \) \( 576 q + 8 q^{9} - 288 q^{25} + 32 q^{26} - 36 q^{33} - 56 q^{36} - 20 q^{38} - 64 q^{42} + 76 q^{44} + 108 q^{48} - 288 q^{49} + 12 q^{56} + 28 q^{60} + 56 q^{66} - 64 q^{69} - 16 q^{77} + 124 q^{78} + 32 q^{80} - 40 q^{81} + 104 q^{86} + 32 q^{89} + 20 q^{92} - 32 q^{93} + 24 q^{97} + O(q^{100}) \)

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

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