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Properties

Label 1800.2.dn
Level $1800$
Weight $2$
Character orbit 1800.dn
Rep. character $\chi_{1800}(113,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1440$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1800.dn (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1800, [\chi])\).

Total New Old
Modular forms 5888 1440 4448
Cusp forms 5632 1440 4192
Eisenstein series 256 0 256

Trace form

\( 1440 q + O(q^{10}) \) \( 1440 q - 12 q^{15} - 24 q^{23} + 12 q^{27} - 12 q^{33} - 40 q^{39} - 64 q^{45} + 36 q^{47} - 40 q^{57} + 4 q^{63} + 72 q^{65} + 36 q^{75} + 48 q^{77} + 60 q^{83} - 24 q^{85} + 40 q^{87} + 84 q^{93} + 60 q^{95} - 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

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