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Properties

Label 2850.2.cg
Level $2850$
Weight $2$
Character orbit 2850.cg
Rep. character $\chi_{2850}(103,\cdot)$
Character field $\Q(\zeta_{60})$
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.cg (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 9728 1600 8128
Cusp forms 9472 1600 7872
Eisenstein series 256 0 256

Trace form

\( 1600 q + 8 q^{5} + 16 q^{7} + O(q^{10}) \) \( 1600 q + 8 q^{5} + 16 q^{7} - 200 q^{16} + 32 q^{17} - 40 q^{19} + 96 q^{22} + 72 q^{23} - 8 q^{28} - 240 q^{29} + 64 q^{30} - 96 q^{33} - 32 q^{35} + 200 q^{36} - 16 q^{38} + 96 q^{43} - 72 q^{47} - 72 q^{53} - 152 q^{55} + 32 q^{57} - 240 q^{59} - 24 q^{60} + 16 q^{62} + 8 q^{63} + 72 q^{67} + 16 q^{68} - 24 q^{70} + 48 q^{73} + 64 q^{77} - 48 q^{78} - 8 q^{80} - 200 q^{81} + 16 q^{82} + 48 q^{83} - 8 q^{85} + 128 q^{87} + 8 q^{92} + 64 q^{93} + 32 q^{95} + 24 q^{97} + 96 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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