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Properties

Label 1980.2.ci
Level $1980$
Weight $2$
Character orbit 1980.ci
Rep. character $\chi_{1980}(373,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $288$
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.ci (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 495 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 1776 288 1488
Cusp forms 1680 288 1392
Eisenstein series 96 0 96

Trace form

\( 288 q + 2 q^{3} + O(q^{10}) \) \( 288 q + 2 q^{3} + 4 q^{11} - 4 q^{15} - 4 q^{23} + 6 q^{25} + 8 q^{27} - 22 q^{33} - 12 q^{37} - 32 q^{45} + 4 q^{47} - 72 q^{53} - 6 q^{67} + 8 q^{71} - 28 q^{75} - 32 q^{77} - 28 q^{81} - 48 q^{91} - 62 q^{93} + 6 q^{97} + O(q^{100}) \)

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

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