Properties

Label 6300.2.da
Level $6300$
Weight $2$
Character orbit 6300.da
Rep. character $\chi_{6300}(199,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $712$
Sturm bound $2880$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 6300 = 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6300.da (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(2880\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6300, [\chi])\).

Total New Old
Modular forms 2976 728 2248
Cusp forms 2784 712 2072
Eisenstein series 192 16 176

Decomposition of \(S_{2}^{\mathrm{new}}(6300, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(6300, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1260, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2100, [\chi])\)\(^{\oplus 2}\)