Properties

Label 672.4.w
Level $672$
Weight $4$
Character orbit 672.w
Rep. character $\chi_{672}(169,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $0$
Newform subspaces $0$
Sturm bound $512$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 672.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 0 \)
Sturm bound: \(512\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(672, [\chi])\).

Total New Old
Modular forms 784 0 784
Cusp forms 752 0 752
Eisenstein series 32 0 32

Decomposition of \(S_{4}^{\mathrm{old}}(672, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(672, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)