Properties

Label 672.4.bu
Level $672$
Weight $4$
Character orbit 672.bu
Rep. character $\chi_{672}(139,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $768$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 672.bu (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 224 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(512\)

Dimensions

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

Total New Old
Modular forms 1552 768 784
Cusp forms 1520 768 752
Eisenstein series 32 0 32

Trace form

\( 768 q + O(q^{10}) \) \( 768 q - 416 q^{14} + 120 q^{16} - 72 q^{18} - 472 q^{22} + 656 q^{23} - 760 q^{28} + 912 q^{35} + 1616 q^{43} - 1000 q^{44} - 5712 q^{50} - 1504 q^{53} + 4032 q^{58} - 2448 q^{60} - 1680 q^{64} - 816 q^{67} + 792 q^{70} + 896 q^{71} - 5992 q^{74} - 7056 q^{78} - 1232 q^{88} - 3600 q^{91} - 13240 q^{92} + 2336 q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(672, [\chi])\) into newform subspaces

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

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

\( S_{4}^{\mathrm{old}}(672, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)