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Properties

Label 2070.4.y
Level $2070$
Weight $4$
Character orbit 2070.y
Rep. character $\chi_{2070}(367,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1728$
Sturm bound $1728$

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Defining parameters

Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2070.y (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1035 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2070, [\chi])\).

Total New Old
Modular forms 5216 1728 3488
Cusp forms 5152 1728 3424
Eisenstein series 64 0 64

Trace form

\( 1728 q + 16 q^{3} - 32 q^{6} + O(q^{10}) \) \( 1728 q + 16 q^{3} - 32 q^{6} + 64 q^{12} + 13824 q^{16} - 32 q^{18} - 568 q^{23} + 576 q^{25} + 592 q^{27} + 448 q^{36} - 1848 q^{41} + 1008 q^{46} + 776 q^{47} + 512 q^{48} + 3168 q^{55} - 9920 q^{71} + 256 q^{72} + 3816 q^{75} - 2176 q^{77} + 3216 q^{78} + 5848 q^{81} + 4208 q^{87} - 2272 q^{92} - 2032 q^{93} + 1464 q^{95} - 256 q^{96} + 5952 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2070, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2070, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2070, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(1035, [\chi])\)\(^{\oplus 2}\)