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Properties

Label 672.4.bc
Level $672$
Weight $4$
Character orbit 672.bc
Rep. character $\chi_{672}(257,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
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.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(512\)

Dimensions

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

Total New Old
Modular forms 800 192 608
Cusp forms 736 192 544
Eisenstein series 64 0 64

Trace form

\( 192 q + O(q^{10}) \) \( 192 q + 136 q^{21} - 2568 q^{25} - 504 q^{37} + 1320 q^{45} + 768 q^{49} - 1696 q^{57} + 648 q^{73} - 2152 q^{81} + 2592 q^{85} - 112 q^{93} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(672, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 5}\)