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Properties

Label 2070.2.n
Level $2070$
Weight $2$
Character orbit 2070.n
Rep. character $\chi_{2070}(689,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $288$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2070.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1035 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2070, [\chi])\).

Total New Old
Modular forms 880 288 592
Cusp forms 848 288 560
Eisenstein series 32 0 32

Trace form

\( 288 q - 144 q^{4} - 8 q^{6} - 12 q^{9} + O(q^{10}) \) \( 288 q - 144 q^{4} - 8 q^{6} - 12 q^{9} - 144 q^{16} + 4 q^{24} + 12 q^{25} - 12 q^{29} - 24 q^{31} + 24 q^{36} + 60 q^{41} - 12 q^{46} - 132 q^{49} + 24 q^{50} + 4 q^{54} + 24 q^{55} + 24 q^{59} + 288 q^{64} - 14 q^{69} - 8 q^{75} - 28 q^{81} - 12 q^{94} - 60 q^{95} + 4 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2070, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2070, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2070, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(1035, [\chi])\)\(^{\oplus 2}\)