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Properties

Label 2700.2.cl
Level $2700$
Weight $2$
Character orbit 2700.cl
Rep. character $\chi_{2700}(169,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $2160$
Sturm bound $1080$

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Defining parameters

Level: \( N \) \(=\) \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2700.cl (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 675 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2700, [\chi])\).

Total New Old
Modular forms 13104 2160 10944
Cusp forms 12816 2160 10656
Eisenstein series 288 0 288

Trace form

\( 2160 q - 12 q^{5} + O(q^{10}) \) \( 2160 q - 12 q^{5} + 51 q^{15} - 36 q^{21} + 36 q^{25} + 18 q^{31} + 9 q^{35} - 30 q^{39} - 159 q^{45} - 75 q^{47} + 9 q^{59} + 69 q^{65} + 90 q^{67} + 33 q^{75} - 240 q^{77} + 36 q^{81} + 150 q^{87} + 42 q^{89} + 90 q^{95} + 60 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2700, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2700, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1350, [\chi])\)\(^{\oplus 2}\)