Properties

Label 6300.2.fi
Level $6300$
Weight $2$
Character orbit 6300.fi
Rep. character $\chi_{6300}(421,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1440$
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.fi (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(2880\)

Dimensions

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

Total New Old
Modular forms 11616 1440 10176
Cusp forms 11424 1440 9984
Eisenstein series 192 0 192

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

\( S_{2}^{\mathrm{old}}(6300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3150, [\chi])\)\(^{\oplus 2}\)