Properties

Label 1200.4.bi
Level $1200$
Weight $4$
Character orbit 1200.bi
Rep. character $\chi_{1200}(857,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $0$
Newform subspaces $0$
Sturm bound $960$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1200.bi (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 0 \)
Sturm bound: \(960\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1200, [\chi])\).

Total New Old
Modular forms 1488 0 1488
Cusp forms 1392 0 1392
Eisenstein series 96 0 96

Decomposition of \(S_{4}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1200, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)