Properties

Label 2850.2.cs
Level $2850$
Weight $2$
Character orbit 2850.cs
Rep. character $\chi_{2850}(13,\cdot)$
Character field $\Q(\zeta_{180})$
Dimension $4800$
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.cs (of order \(180\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{180})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 29184 4800 24384
Cusp forms 28416 4800 23616
Eisenstein series 768 0 768

Trace form

\( 4800q - 24q^{7} + O(q^{10}) \) \( 4800q - 24q^{7} - 96q^{22} - 192q^{23} - 24q^{25} + 240q^{29} + 96q^{33} + 360q^{43} + 192q^{47} + 72q^{53} - 72q^{55} - 24q^{57} + 240q^{59} + 24q^{60} - 48q^{62} - 144q^{67} - 24q^{68} - 48q^{70} - 72q^{73} + 48q^{78} + 96q^{82} + 168q^{83} + 384q^{85} + 96q^{87} + 96q^{92} + 48q^{95} + 192q^{97} + 192q^{98} + O(q^{100}) \)

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

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