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Properties

Label 2070.4.j
Level $2070$
Weight $4$
Character orbit 2070.j
Rep. character $\chi_{2070}(323,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $264$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 2624 264 2360
Cusp forms 2560 264 2296
Eisenstein series 64 0 64

Trace form

\( 264 q + 48 q^{7} + O(q^{10}) \) \( 264 q + 48 q^{7} + 96 q^{10} - 24 q^{13} - 4224 q^{16} + 672 q^{22} + 192 q^{28} - 1152 q^{31} + 264 q^{37} - 192 q^{40} + 96 q^{52} + 1200 q^{55} + 1776 q^{58} + 6912 q^{61} - 1152 q^{67} - 2976 q^{70} + 5256 q^{73} - 4608 q^{76} + 624 q^{82} + 864 q^{85} + 2688 q^{88} + 14400 q^{91} - 3384 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2070, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1035, [\chi])\)\(^{\oplus 2}\)