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Properties

Label 2700.2.w
Level $2700$
Weight $2$
Character orbit 2700.w
Rep. character $\chi_{2700}(431,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $960$
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.w (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 300 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1080\)

Dimensions

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

Total New Old
Modular forms 2208 960 1248
Cusp forms 2112 960 1152
Eisenstein series 96 0 96

Trace form

\( 960 q + 4 q^{10} - 12 q^{16} - 8 q^{22} + 4 q^{25} - 16 q^{28} - 16 q^{34} - 48 q^{37} - 6 q^{40} - 20 q^{46} - 968 q^{49} - 38 q^{52} - 20 q^{58} - 32 q^{61} + 24 q^{64} - 42 q^{70} - 8 q^{73} - 96 q^{76}+ \cdots - 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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

\( S_{2}^{\mathrm{old}}(2700, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)