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Properties

Label 2790.2.eo
Level $2790$
Weight $2$
Character orbit 2790.eo
Rep. character $\chi_{2790}(173,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3072$
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.eo (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1395 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 9344 3072 6272
Cusp forms 9088 3072 6016
Eisenstein series 256 0 256

Trace form

\( 3072 q + 16 q^{3} + O(q^{10}) \) \( 3072 q + 16 q^{3} + 8 q^{12} + 4 q^{15} - 384 q^{16} - 12 q^{25} + 124 q^{27} + 48 q^{30} - 88 q^{33} - 48 q^{37} - 108 q^{38} + 48 q^{41} - 24 q^{42} + 40 q^{45} + 48 q^{47} - 12 q^{48} + 16 q^{51} - 12 q^{53} + 12 q^{55} + 80 q^{57} + 12 q^{58} + 36 q^{60} - 36 q^{62} + 224 q^{63} + 16 q^{66} - 12 q^{67} + 120 q^{71} + 176 q^{75} + 16 q^{78} - 192 q^{81} + 80 q^{87} + 44 q^{90} + 96 q^{93} + 60 q^{95} + 108 q^{97} + 288 q^{98} + O(q^{100}) \)

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

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