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Properties

Label 672.4.bs
Level $672$
Weight $4$
Character orbit 672.bs
Rep. character $\chi_{672}(155,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $1152$
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.bs (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
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 1152 400
Cusp forms 1520 1152 368
Eisenstein series 32 0 32

Trace form

\( 1152 q + O(q^{10}) \) \( 1152 q + 240 q^{10} - 480 q^{16} + 864 q^{22} - 528 q^{27} + 1160 q^{30} - 1600 q^{36} + 1200 q^{39} + 2880 q^{46} + 4888 q^{48} + 1728 q^{52} - 576 q^{55} + 4752 q^{58} - 6104 q^{60} - 3648 q^{61} + 6592 q^{66} + 3264 q^{67} + 1008 q^{70} - 2760 q^{72} - 10416 q^{76} + 5064 q^{78} - 11328 q^{79} + 2576 q^{87} - 3120 q^{88} + 3720 q^{90} - 8928 q^{94} + 12352 q^{96} + 10624 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{4}^{\mathrm{old}}(672, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)