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Properties

Label 2790.2.ck
Level $2790$
Weight $2$
Character orbit 2790.ck
Rep. character $\chi_{2790}(563,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $768$
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.ck (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1395 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 2336 768 1568
Cusp forms 2272 768 1504
Eisenstein series 64 0 64

Trace form

\( 768 q + 8 q^{3} + O(q^{10}) \) \( 768 q + 8 q^{3} + 16 q^{12} - 4 q^{15} + 384 q^{16} - 12 q^{20} - 24 q^{25} - 4 q^{27} - 48 q^{30} + 28 q^{33} - 12 q^{37} - 12 q^{42} - 40 q^{45} - 48 q^{47} - 8 q^{48} - 16 q^{51} - 12 q^{53} - 12 q^{55} + 40 q^{57} - 12 q^{58} + 4 q^{60} - 36 q^{62} + 56 q^{63} - 16 q^{66} - 24 q^{67} + 120 q^{71} - 4 q^{75} + 44 q^{78} - 96 q^{81} - 120 q^{83} - 20 q^{87} + 52 q^{90} + 160 q^{93} - 60 q^{95} + 12 q^{97} - 72 q^{98} + O(q^{100}) \)

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

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