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Properties

Label 2070.4.z
Level $2070$
Weight $4$
Character orbit 2070.z
Rep. character $\chi_{2070}(89,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1440$
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.z (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 345 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 13120 1440 11680
Cusp forms 12800 1440 11360
Eisenstein series 320 0 320

Trace form

\( 1440 q - 576 q^{4} + O(q^{10}) \) \( 1440 q - 576 q^{4} - 2304 q^{16} - 528 q^{25} + 432 q^{31} - 720 q^{46} - 4752 q^{49} + 7488 q^{55} + 2112 q^{61} - 9216 q^{64} - 6816 q^{70} + 7392 q^{79} + 14832 q^{85} + 4032 q^{94} + O(q^{100}) \)

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

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