Properties

Label 7200.2.bw
Level $7200$
Weight $2$
Character orbit 7200.bw
Rep. character $\chi_{7200}(1201,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $444$
Sturm bound $2880$

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Defining parameters

Level: \( N \) \(=\) \( 7200 = 2^{5} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7200.bw (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(2880\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(7200, [\chi])\).

Total New Old
Modular forms 2976 468 2508
Cusp forms 2784 444 2340
Eisenstein series 192 24 168

Decomposition of \(S_{2}^{\mathrm{new}}(7200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(7200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(7200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 3}\)