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Properties

Label 2070.4.d
Level $2070$
Weight $4$
Character orbit 2070.d
Rep. character $\chi_{2070}(829,\cdot)$
Character field $\Q$
Dimension $164$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Sturm bound: \(1728\)

Dimensions

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

Total New Old
Modular forms 1312 164 1148
Cusp forms 1280 164 1116
Eisenstein series 32 0 32

Trace form

\( 164 q - 656 q^{4} - 12 q^{5} + O(q^{10}) \) \( 164 q - 656 q^{4} - 12 q^{5} - 8 q^{10} - 16 q^{11} + 2624 q^{16} + 288 q^{19} + 48 q^{20} + 112 q^{25} + 680 q^{26} - 1148 q^{29} - 176 q^{31} - 112 q^{34} + 1492 q^{35} + 32 q^{40} + 128 q^{41} + 64 q^{44} - 184 q^{46} - 8260 q^{49} - 648 q^{50} - 1496 q^{55} + 908 q^{59} + 2128 q^{61} - 10496 q^{64} - 860 q^{65} + 1224 q^{70} - 4208 q^{71} + 288 q^{74} - 1152 q^{76} - 1544 q^{79} - 192 q^{80} + 1452 q^{85} + 2224 q^{86} + 8040 q^{89} + 6960 q^{91} + 1136 q^{94} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2070, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)