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Properties

Label 1800.2.dh
Level $1800$
Weight $2$
Character orbit 1800.dh
Rep. character $\chi_{1800}(169,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $720$
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.dh (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 2944 720 2224
Cusp forms 2816 720 2096
Eisenstein series 128 0 128

Trace form

\( 720 q + O(q^{10}) \) \( 720 q - 12 q^{11} + 38 q^{15} - 12 q^{29} - 12 q^{35} + 12 q^{39} + 16 q^{41} + 74 q^{45} + 360 q^{49} + 12 q^{51} - 12 q^{55} + 36 q^{59} + 20 q^{63} - 18 q^{65} + 12 q^{69} + 10 q^{75} - 12 q^{79} - 72 q^{81} - 12 q^{85} + 100 q^{87} + 48 q^{89} + 36 q^{95} + 40 q^{99} + O(q^{100}) \)

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

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