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Properties

Label 2070.4.bt
Level $2070$
Weight $4$
Character orbit 2070.bt
Rep. character $\chi_{2070}(77,\cdot)$
Character field $\Q(\zeta_{132})$
Dimension $17280$
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.bt (of order \(132\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1035 \)
Character field: \(\Q(\zeta_{132})\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 52160 17280 34880
Cusp forms 51520 17280 34240
Eisenstein series 640 0 640

Trace form

\( 17280 q + 16 q^{3} - 32 q^{6} + O(q^{10}) \) \( 17280 q + 16 q^{3} - 32 q^{6} - 64 q^{12} - 8 q^{15} - 13824 q^{16} + 144 q^{18} + 384 q^{20} + 480 q^{21} + 312 q^{23} - 576 q^{25} + 592 q^{27} + 6336 q^{33} - 448 q^{36} + 576 q^{37} + 5544 q^{41} - 1008 q^{46} + 2328 q^{47} + 512 q^{48} + 128 q^{51} + 3168 q^{55} + 9504 q^{56} - 848 q^{57} + 1792 q^{60} + 72 q^{61} - 9072 q^{63} - 1392 q^{65} - 8928 q^{66} + 2448 q^{67} - 256 q^{72} - 8884 q^{75} - 6528 q^{77} + 3216 q^{78} + 11816 q^{81} + 5640 q^{83} + 4208 q^{87} + 2960 q^{90} + 1248 q^{92} + 12752 q^{93} + 7080 q^{95} - 256 q^{96} - 20736 q^{97} + O(q^{100}) \)

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

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