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Properties

Label 1800.4.dh
Level $1800$
Weight $4$
Character orbit 1800.dh
Rep. character $\chi_{1800}(169,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $2160$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1800.dh (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1800, [\chi])\).

Total New Old
Modular forms 8704 2160 6544
Cusp forms 8576 2160 6416
Eisenstein series 128 0 128

Trace form

\( 2160 q + O(q^{10}) \) \( 2160 q + 132 q^{11} - 346 q^{15} + 348 q^{29} - 12 q^{35} + 732 q^{39} - 656 q^{41} + 230 q^{45} + 52920 q^{49} + 588 q^{51} + 612 q^{55} - 2124 q^{59} + 2660 q^{63} - 126 q^{65} + 372 q^{69} + 2026 q^{75} - 252 q^{79} - 1368 q^{81} + 828 q^{85} - 8300 q^{87} - 4272 q^{89} + 2124 q^{95} + 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)