Properties

Label 6300.2.ix
Level $6300$
Weight $2$
Character orbit 6300.ix
Rep. character $\chi_{6300}(733,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3840$
Sturm bound $2880$

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Defining parameters

Level: \( N \) \(=\) \( 6300 = 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6300.ix (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1575 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(2880\)

Dimensions

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

Total New Old
Modular forms 23232 3840 19392
Cusp forms 22848 3840 19008
Eisenstein series 384 0 384

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

\( S_{2}^{\mathrm{old}}(6300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3150, [\chi])\)\(^{\oplus 2}\)