Properties

Label 1980.2.cx
Level $1980$
Weight $2$
Character orbit 1980.cx
Rep. character $\chi_{1980}(49,\cdot)$
Character field $\Q(\zeta_{30})$
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.cx (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 495 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 3552 576 2976
Cusp forms 3360 576 2784
Eisenstein series 192 0 192

Trace form

\( 576 q - q^{5} + 10 q^{9} + O(q^{10}) \) \( 576 q - q^{5} + 10 q^{9} + 2 q^{11} - 4 q^{21} + 3 q^{25} + 32 q^{29} - 6 q^{31} - 30 q^{35} + 20 q^{39} - 32 q^{41} + 54 q^{45} - 72 q^{49} - 64 q^{51} + 12 q^{55} - 34 q^{59} + 12 q^{65} + 38 q^{69} - 4 q^{71} - 13 q^{75} + 12 q^{79} - 102 q^{81} + 120 q^{89} + 36 q^{91} - 8 q^{95} + 188 q^{99} + O(q^{100}) \)

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

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