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Properties

Label 2790.2.dk
Level $2790$
Weight $2$
Character orbit 2790.dk
Rep. character $\chi_{2790}(29,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1536$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2790.dk (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1395 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2790, [\chi])\).

Total New Old
Modular forms 4672 1536 3136
Cusp forms 4544 1536 3008
Eisenstein series 128 0 128

Trace form

\( 1536 q + 192 q^{4} + 12 q^{5} + 8 q^{9} + O(q^{10}) \) \( 1536 q + 192 q^{4} + 12 q^{5} + 8 q^{9} - 20 q^{15} + 192 q^{16} - 12 q^{20} - 12 q^{25} - 48 q^{31} - 16 q^{36} - 8 q^{39} - 24 q^{41} + 54 q^{45} - 192 q^{49} - 92 q^{51} + 24 q^{59} - 10 q^{60} - 384 q^{64} + 16 q^{66} + 8 q^{69} - 12 q^{70} - 100 q^{75} - 32 q^{90} + 204 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2790, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2790, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2790, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1395, [\chi])\)\(^{\oplus 2}\)