Properties

Label 2850.2.t
Level $2850$
Weight $2$
Character orbit 2850.t
Rep. character $\chi_{2850}(2501,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $256$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 1248 256 992
Cusp forms 1152 256 896
Eisenstein series 96 0 96

Trace form

\( 256q - 3q^{3} - 128q^{4} - q^{6} + 12q^{7} + q^{9} + O(q^{10}) \) \( 256q - 3q^{3} - 128q^{4} - q^{6} + 12q^{7} + q^{9} - 18q^{13} - 128q^{16} - 18q^{19} - 30q^{22} - q^{24} - 6q^{28} + 33q^{33} + 12q^{34} + q^{36} - 10q^{42} + 42q^{43} + 3q^{48} + 284q^{49} - 18q^{51} + 18q^{52} + 44q^{54} - 28q^{57} - 38q^{61} - 20q^{63} + 256q^{64} - q^{66} + 60q^{67} + 3q^{72} + 8q^{73} + 24q^{76} + 30q^{78} - 42q^{79} + 57q^{81} - 6q^{82} + 60q^{87} - 114q^{91} - 10q^{93} + 2q^{96} - 30q^{97} + 29q^{99} + O(q^{100}) \)

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

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