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Properties

Label 1620.4.bb
Level $1620$
Weight $4$
Character orbit 1620.bb
Rep. character $\chi_{1620}(179,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1920$
Sturm bound $1296$

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Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1620.bb (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 540 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1296\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1620, [\chi])\).

Total New Old
Modular forms 5904 1968 3936
Cusp forms 5760 1920 3840
Eisenstein series 144 48 96

Trace form

\( 1920 q - 12 q^{4} + 12 q^{5} + O(q^{10}) \) \( 1920 q - 12 q^{4} + 12 q^{5} - 3 q^{10} + 12 q^{14} - 12 q^{16} + 237 q^{20} - 12 q^{25} - 60 q^{29} + 36 q^{34} + 369 q^{40} + 24 q^{41} + 2682 q^{44} - 6 q^{46} - 24 q^{49} - 3192 q^{50} + 6018 q^{56} - 24 q^{61} - 6 q^{64} + 708 q^{65} + 999 q^{70} + 6402 q^{74} - 396 q^{76} + 738 q^{85} + 4194 q^{86} + 36 q^{89} - 12 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1620, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1620, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)