Properties

Label 2850.2.bc
Level $2850$
Weight $2$
Character orbit 2850.bc
Rep. character $\chi_{2850}(341,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $800$
Sturm bound $1200$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2850.bc (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1425 \)
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 800 1632
Cusp forms 2368 800 1568
Eisenstein series 64 0 64

Trace form

\( 800q - 200q^{4} + O(q^{10}) \) \( 800q - 200q^{4} - 200q^{16} + 12q^{19} - 40q^{25} + 4q^{30} - 24q^{39} + 32q^{42} - 16q^{43} - 16q^{45} + 832q^{49} + 24q^{54} - 16q^{55} + 48q^{57} + 48q^{61} - 200q^{64} - 32q^{66} + 80q^{73} - 8q^{76} + 88q^{81} + 8q^{85} - 80q^{87} - 8q^{93} + 64q^{99} + O(q^{100}) \)

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

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