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Properties

Label 2070.2.k
Level $2070$
Weight $2$
Character orbit 2070.k
Rep. character $\chi_{2070}(1333,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $120$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(i)\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 896 120 776
Cusp forms 832 120 712
Eisenstein series 64 0 64

Trace form

\( 120 q + O(q^{10}) \) \( 120 q + 16 q^{13} - 120 q^{16} - 32 q^{25} + 8 q^{26} + 8 q^{31} + 8 q^{35} - 24 q^{41} + 24 q^{46} - 24 q^{47} - 8 q^{50} + 16 q^{52} - 32 q^{55} + 32 q^{62} + 72 q^{70} + 56 q^{71} - 40 q^{73} - 40 q^{77} + 24 q^{82} - 72 q^{85} + 48 q^{95} - 32 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2070, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1035, [\chi])\)\(^{\oplus 2}\)