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Properties

Label 2070.4.br
Level $2070$
Weight $4$
Character orbit 2070.br
Rep. character $\chi_{2070}(149,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $8640$
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.br (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1035 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 26080 8640 17440
Cusp forms 25760 8640 17120
Eisenstein series 320 0 320

Trace form

\( 8640 q + 1728 q^{4} - 16 q^{6} + 156 q^{9} + O(q^{10}) \) \( 8640 q + 1728 q^{4} - 16 q^{6} + 156 q^{9} + 1496 q^{15} + 6912 q^{16} + 32 q^{24} + 288 q^{25} + 84 q^{29} - 1496 q^{30} - 144 q^{31} - 1248 q^{36} + 1584 q^{39} + 300 q^{41} - 504 q^{46} + 19386 q^{49} - 2256 q^{50} + 2556 q^{54} - 1584 q^{55} - 5808 q^{56} - 3984 q^{59} + 88 q^{60} - 55296 q^{64} - 25872 q^{65} + 5456 q^{66} - 13206 q^{69} - 10032 q^{74} - 1766 q^{75} - 3940 q^{81} + 3784 q^{84} + 1224 q^{94} - 3540 q^{95} + 128 q^{96} + O(q^{100}) \)

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

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