Properties

Label 2850.2.bd
Level $2850$
Weight $2$
Character orbit 2850.bd
Rep. character $\chi_{2850}(1493,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $480$
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.bd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 285 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 2496 480 2016
Cusp forms 2304 480 1824
Eisenstein series 192 0 192

Trace form

\( 480q + O(q^{10}) \) \( 480q + 16q^{13} + 240q^{16} - 32q^{18} + 8q^{22} - 24q^{27} + 16q^{31} - 12q^{33} + 16q^{37} + 32q^{42} + 40q^{43} - 44q^{51} - 16q^{52} + 92q^{57} + 8q^{61} - 28q^{63} + 44q^{66} + 24q^{67} - 16q^{72} - 64q^{73} - 8q^{76} - 16q^{78} + 232q^{87} - 16q^{88} - 40q^{91} + 20q^{93} + 16q^{97} + O(q^{100}) \)

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

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