↑

Properties

Label 588.4.o
Level $588$
Weight $4$
Character orbit 588.o
Rep. character $\chi_{588}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $240$
Sturm bound $448$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 588.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(588, [\chi])\).

Total New Old
Modular forms 704 240 464
Cusp forms 640 240 400
Eisenstein series 64 0 64

Trace form

\( 240 q + 4 q^{2} + 20 q^{4} + 220 q^{8} - 1080 q^{9} + O(q^{10}) \) \( 240 q + 4 q^{2} + 20 q^{4} + 220 q^{8} - 1080 q^{9} - 18 q^{10} - 116 q^{16} + 36 q^{18} + 196 q^{22} + 270 q^{24} + 2916 q^{25} + 750 q^{26} - 1600 q^{29} + 168 q^{30} - 286 q^{32} + 36 q^{33} - 360 q^{36} + 284 q^{37} - 1494 q^{38} - 1170 q^{40} - 2320 q^{44} + 776 q^{46} - 1792 q^{50} + 3564 q^{52} + 1896 q^{53} + 504 q^{57} + 3670 q^{58} - 1014 q^{60} + 600 q^{61} + 1880 q^{64} - 280 q^{65} - 2052 q^{66} - 7452 q^{68} - 990 q^{72} + 972 q^{73} + 1098 q^{74} - 1620 q^{78} + 5976 q^{80} - 9720 q^{81} + 9816 q^{82} - 4944 q^{85} + 18 q^{86} + 3114 q^{88} + 10864 q^{92} - 12 q^{93} - 9072 q^{94} - 3870 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(588, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(588, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(588, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)