Properties

Label 2850.2.x
Level $2850$
Weight $2$
Character orbit 2850.x
Rep. character $\chi_{2850}(229,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $352$
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.x (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 2432 352 2080
Cusp forms 2368 352 2016
Eisenstein series 64 0 64

Trace form

\( 352q + 88q^{4} - 4q^{5} + 4q^{6} + 88q^{9} + O(q^{10}) \) \( 352q + 88q^{4} - 4q^{5} + 4q^{6} + 88q^{9} - 4q^{10} - 12q^{11} - 4q^{15} - 88q^{16} + 20q^{17} - 4q^{19} + 4q^{20} - 20q^{23} + 16q^{24} - 16q^{26} + 20q^{28} + 16q^{29} - 12q^{31} - 24q^{34} - 4q^{35} - 88q^{36} + 4q^{40} - 88q^{41} - 20q^{42} - 8q^{44} + 4q^{45} - 304q^{49} + 16q^{50} + 80q^{53} - 4q^{54} - 16q^{55} - 16q^{60} + 16q^{61} - 120q^{62} - 20q^{63} + 88q^{64} - 32q^{65} + 16q^{66} + 20q^{70} + 80q^{73} - 16q^{74} - 16q^{76} + 40q^{79} - 4q^{80} - 88q^{81} + 20q^{83} - 92q^{85} + 48q^{86} - 20q^{88} - 24q^{89} + 4q^{90} + 8q^{91} - 4q^{95} + 4q^{96} + 20q^{97} - 8q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1425, [\chi])\)\(^{\oplus 2}\)