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Properties

Label 2070.2.bc
Level $2070$
Weight $2$
Character orbit 2070.bc
Rep. character $\chi_{2070}(251,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $320$
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.bc (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 4480 320 4160
Cusp forms 4160 320 3840
Eisenstein series 320 0 320

Trace form

\( 320 q + 32 q^{4} + O(q^{10}) \) \( 320 q + 32 q^{4} - 32 q^{16} - 32 q^{25} + 16 q^{31} - 176 q^{43} + 8 q^{46} + 32 q^{49} - 40 q^{55} + 144 q^{58} + 176 q^{61} + 32 q^{64} + 176 q^{67} + 112 q^{73} + 176 q^{79} + 112 q^{82} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2070, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(414, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1035, [\chi])\)\(^{\oplus 2}\)