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Properties

Label 1980.2.ba
Level $1980$
Weight $2$
Character orbit 1980.ba
Rep. character $\chi_{1980}(329,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $144$
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.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 495 \)
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 888 144 744
Cusp forms 840 144 696
Eisenstein series 48 0 48

Trace form

\( 144 q + 3 q^{5} - 6 q^{9} + O(q^{10}) \) \( 144 q + 3 q^{5} - 6 q^{9} - 6 q^{11} + 4 q^{15} - 3 q^{25} - 6 q^{31} - 21 q^{45} - 72 q^{49} + 12 q^{55} + 78 q^{59} + 22 q^{69} - 13 q^{75} + 2 q^{81} + 24 q^{91} - 52 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1980, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(990, [\chi])\)\(^{\oplus 2}\)