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Properties

Label 720.4.bw
Level $720$
Weight $4$
Character orbit 720.bw
Rep. character $\chi_{720}(191,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $144$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 720.bw (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(720, [\chi])\).

Total New Old
Modular forms 888 144 744
Cusp forms 840 144 696
Eisenstein series 48 0 48

Trace form

\( 144 q + 60 q^{9} + O(q^{10}) \) \( 144 q + 60 q^{9} - 204 q^{21} + 1800 q^{25} + 252 q^{29} + 108 q^{33} - 180 q^{41} + 1320 q^{45} + 3528 q^{49} - 2820 q^{57} + 4716 q^{69} - 4968 q^{73} + 5904 q^{77} + 2304 q^{81} - 336 q^{93} + 108 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(720, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(720, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(720, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)