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Properties

Label 1980.2.bw
Level $1980$
Weight $2$
Character orbit 1980.bw
Rep. character $\chi_{1980}(19,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $704$
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.bw (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 220 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 1792 736 1056
Cusp forms 1664 704 960
Eisenstein series 128 32 96

Trace form

\( 704 q - 6 q^{4} + 6 q^{5} + O(q^{10}) \) \( 704 q - 6 q^{4} + 6 q^{5} + 10 q^{14} + 22 q^{16} + 10 q^{20} + 2 q^{25} - 12 q^{26} + 20 q^{29} + 8 q^{34} + 30 q^{40} + 40 q^{41} + 86 q^{44} - 90 q^{46} + 144 q^{49} + 40 q^{50} + 32 q^{56} - 20 q^{61} + 30 q^{64} + 58 q^{70} + 80 q^{74} + 32 q^{80} - 50 q^{85} - 6 q^{86} + 40 q^{89} + 60 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1980, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)