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Properties

Label 2790.2.dz
Level $2790$
Weight $2$
Character orbit 2790.dz
Rep. character $\chi_{2790}(49,\cdot)$
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.dz (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

\( 1536 q - 192 q^{4} + 4 q^{5} + 8 q^{9} + O(q^{10}) \) \( 1536 q - 192 q^{4} + 4 q^{5} + 8 q^{9} - 8 q^{11} + 4 q^{15} + 192 q^{16} + 2 q^{20} - 12 q^{25} + 96 q^{26} + 24 q^{29} - 18 q^{30} - 48 q^{31} - 12 q^{35} - 8 q^{36} - 8 q^{39} + 16 q^{41} + 8 q^{44} + 4 q^{45} + 384 q^{49} + 40 q^{51} + 24 q^{54} + 12 q^{55} - 12 q^{59} - 10 q^{60} + 384 q^{64} - 20 q^{65} - 8 q^{66} - 84 q^{69} + 6 q^{70} + 20 q^{71} - 64 q^{74} + 172 q^{75} - 48 q^{79} + 18 q^{80} + 16 q^{81} - 40 q^{86} - 176 q^{89} + 116 q^{90} - 38 q^{95} + 20 q^{99} + O(q^{100}) \)

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

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