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Properties

Label 2700.2.o
Level $2700$
Weight $2$
Character orbit 2700.o
Rep. character $\chi_{2700}(899,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $208$
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.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 180 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1080\)

Dimensions

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

Total New Old
Modular forms 1152 224 928
Cusp forms 1008 208 800
Eisenstein series 144 16 128

Trace form

\( 208 q + 2 q^{4} + O(q^{10}) \) \( 208 q + 2 q^{4} - 6 q^{14} - 2 q^{16} - 36 q^{29} + 10 q^{34} + 12 q^{41} - 24 q^{46} - 76 q^{49} + 132 q^{56} - 4 q^{61} + 32 q^{64} + 24 q^{74} + 18 q^{76} + 174 q^{86} + 18 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)