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Properties

Label 570.4.x
Level $570$
Weight $4$
Character orbit 570.x
Rep. character $\chi_{570}(103,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $240$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 570.x (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(570, [\chi])\).

Total New Old
Modular forms 1472 240 1232
Cusp forms 1408 240 1168
Eisenstein series 64 0 64

Trace form

\( 240 q + 32 q^{5} - 32 q^{7} + O(q^{10}) \) \( 240 q + 32 q^{5} - 32 q^{7} - 112 q^{11} + 1920 q^{16} + 256 q^{17} - 576 q^{21} - 432 q^{22} - 296 q^{23} + 520 q^{25} + 1216 q^{26} + 64 q^{28} + 96 q^{30} - 1152 q^{33} - 688 q^{35} - 4320 q^{36} - 352 q^{38} + 888 q^{41} - 2288 q^{43} + 1664 q^{47} - 3744 q^{53} - 568 q^{55} - 624 q^{57} - 576 q^{60} + 1728 q^{61} - 32 q^{62} - 144 q^{63} + 5496 q^{67} - 2048 q^{68} + 3024 q^{70} + 2016 q^{73} + 2240 q^{76} - 2768 q^{77} - 2016 q^{78} - 512 q^{80} + 9720 q^{81} - 992 q^{82} + 1136 q^{83} - 2792 q^{85} + 1056 q^{86} + 1824 q^{87} + 13872 q^{91} + 1184 q^{92} - 912 q^{93} + 5728 q^{95} + 9792 q^{97} + 7872 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(570, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(570, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(570, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)