Properties

Label 2850.2.bw
Level $2850$
Weight $2$
Character orbit 2850.bw
Rep. character $\chi_{2850}(179,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1600$
Sturm bound $1200$

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Defining parameters

Level: \( N \) \(=\) \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2850.bw (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1425 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2850, [\chi])\).

Total New Old
Modular forms 4864 1600 3264
Cusp forms 4736 1600 3136
Eisenstein series 128 0 128

Trace form

\( 1600q - 200q^{4} + O(q^{10}) \) \( 1600q - 200q^{4} + 30q^{15} + 200q^{16} - 12q^{19} + 60q^{22} + 12q^{25} + 4q^{30} + 24q^{39} + 28q^{45} - 1536q^{49} + 60q^{51} + 12q^{54} - 12q^{55} - 30q^{60} - 24q^{61} + 40q^{63} + 400q^{64} + 16q^{66} - 36q^{70} + 80q^{73} - 8q^{76} - 8q^{81} - 32q^{85} + 54q^{90} + 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2850, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1425, [\chi])\)\(^{\oplus 2}\)