↑

Properties

Label 1980.2.cl
Level $1980$
Weight $2$
Character orbit 1980.cl
Rep. character $\chi_{1980}(67,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1440$
Sturm bound $864$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1980.cl (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 180 \)
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 1760 1440 320
Cusp forms 1696 1440 256
Eisenstein series 64 0 64

Trace form

\( 1440 q + O(q^{10}) \) \( 1440 q + 56 q^{18} + 16 q^{21} + 40 q^{30} - 40 q^{32} + 56 q^{38} - 80 q^{42} + 48 q^{46} + 24 q^{48} - 80 q^{50} + 48 q^{53} + 32 q^{57} - 80 q^{60} - 32 q^{65} - 104 q^{68} - 40 q^{72} + 24 q^{76} - 180 q^{78} - 80 q^{81} - 72 q^{86} + 48 q^{93} - 144 q^{96} - 304 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1980, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)