↑

Properties

Label 2070.2.bt
Level $2070$
Weight $2$
Character orbit 2070.bt
Rep. character $\chi_{2070}(77,\cdot)$
Character field $\Q(\zeta_{132})$
Dimension $5760$
Sturm bound $864$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2070.bt (of order \(132\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1035 \)
Character field: \(\Q(\zeta_{132})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 17600 5760 11840
Cusp forms 16960 5760 11200
Eisenstein series 640 0 640

Trace form

\( 5760 q - 8 q^{3} + 16 q^{6} + O(q^{10}) \) \( 5760 q - 8 q^{3} + 16 q^{6} + 8 q^{12} - 8 q^{15} - 288 q^{16} - 72 q^{18} + 24 q^{20} + 24 q^{23} + 24 q^{25} + 16 q^{27} + 72 q^{33} - 16 q^{36} + 48 q^{37} - 72 q^{41} + 24 q^{46} + 24 q^{47} - 16 q^{48} - 64 q^{51} + 48 q^{55} + 108 q^{56} + 16 q^{57} - 8 q^{60} + 24 q^{61} + 96 q^{63} + 48 q^{65} + 144 q^{66} + 24 q^{67} + 32 q^{72} - 4 q^{75} + 96 q^{77} + 72 q^{78} + 152 q^{81} - 120 q^{83} - 16 q^{87} - 40 q^{90} + 24 q^{92} - 16 q^{93} - 120 q^{95} + 8 q^{96} - 108 q^{97} + O(q^{100}) \)

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

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