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Properties

Label 2070.2.r
Level $2070$
Weight $2$
Character orbit 2070.r
Rep. character $\chi_{2070}(139,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $264$
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.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 880 264 616
Cusp forms 848 264 584
Eisenstein series 32 0 32

Trace form

\( 264 q + 132 q^{4} + 16 q^{9} + O(q^{10}) \) \( 264 q + 132 q^{4} + 16 q^{9} - 8 q^{11} + 12 q^{15} - 132 q^{16} + 56 q^{21} + 48 q^{26} + 8 q^{29} - 36 q^{30} - 64 q^{35} + 8 q^{36} - 72 q^{39} - 32 q^{41} - 16 q^{44} - 8 q^{45} + 132 q^{49} - 16 q^{50} - 96 q^{51} - 72 q^{54} + 24 q^{55} + 48 q^{59} + 24 q^{60} - 264 q^{64} + 52 q^{65} - 8 q^{66} - 12 q^{70} - 32 q^{71} + 40 q^{75} + 48 q^{79} - 48 q^{81} + 40 q^{84} + 24 q^{85} - 24 q^{86} + 80 q^{89} + 28 q^{90} + 48 q^{91} + 76 q^{95} + 112 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2070, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1035, [\chi])\)\(^{\oplus 2}\)