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Properties

Label 720.4.by
Level $720$
Weight $4$
Character orbit 720.by
Rep. character $\chi_{720}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $212$
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.by (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 888 220 668
Cusp forms 840 212 628
Eisenstein series 48 8 40

Trace form

\( 212 q - q^{5} - 4 q^{9} + O(q^{10}) \) \( 212 q - q^{5} - 4 q^{9} + 134 q^{11} + 35 q^{15} + 8 q^{19} + 10 q^{21} - q^{25} - 30 q^{29} + 2 q^{31} + 254 q^{35} - 494 q^{39} - 2 q^{41} + 123 q^{45} + 4604 q^{49} + 52 q^{51} - 246 q^{55} - 2122 q^{59} - 2 q^{61} - 483 q^{65} + 450 q^{69} + 5736 q^{71} - 339 q^{75} + 2 q^{79} - 920 q^{81} + 124 q^{85} + 416 q^{89} + 1380 q^{91} + 1008 q^{95} - 4666 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(720, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)