Properties

Label 2850.2.f
Level $2850$
Weight $2$
Character orbit 2850.f
Rep. character $\chi_{2850}(2051,\cdot)$
Character field $\Q$
Dimension $128$
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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 624 128 496
Cusp forms 576 128 448
Eisenstein series 48 0 48

Trace form

\( 128q + 128q^{4} - 2q^{6} - 12q^{7} + 2q^{9} + O(q^{10}) \) \( 128q + 128q^{4} - 2q^{6} - 12q^{7} + 2q^{9} + 128q^{16} - 24q^{19} - 2q^{24} - 12q^{28} + 2q^{36} + 30q^{39} + 10q^{42} + 172q^{49} - 8q^{54} - 14q^{57} + 12q^{58} - 64q^{61} + 62q^{63} + 128q^{64} - 8q^{66} + 28q^{73} - 24q^{76} + 66q^{81} + 42q^{87} + 4q^{93} - 2q^{96} + 40q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1425, [\chi])\)\(^{\oplus 2}\)