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Properties

Label 588.4.x
Level $588$
Weight $4$
Character orbit 588.x
Rep. character $\chi_{588}(55,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1008$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 588.x (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 196 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 2040 1008 1032
Cusp forms 1992 1008 984
Eisenstein series 48 0 48

Trace form

\( 1008 q - 84 q^{8} - 1512 q^{9} + O(q^{10}) \) \( 1008 q - 84 q^{8} - 1512 q^{9} - 170 q^{14} - 112 q^{16} + 60 q^{21} + 252 q^{22} + 630 q^{24} + 4032 q^{25} + 196 q^{28} + 336 q^{30} + 140 q^{32} - 2128 q^{34} - 1260 q^{37} + 504 q^{40} - 96 q^{42} + 3080 q^{44} - 1120 q^{46} + 848 q^{49} - 9156 q^{50} + 784 q^{53} + 1766 q^{56} - 504 q^{57} + 2380 q^{58} + 420 q^{60} - 3780 q^{61} - 4704 q^{64} - 560 q^{65} + 10 q^{70} + 1890 q^{72} - 2156 q^{74} + 2142 q^{76} - 1936 q^{77} + 1764 q^{78} - 13608 q^{81} - 3920 q^{82} + 2064 q^{84} + 2352 q^{85} - 392 q^{86} + 3388 q^{88} - 6986 q^{92} - 1848 q^{93} + 6930 q^{94} + 4732 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(588, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)