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Properties

Label 570.4.m
Level $570$
Weight $4$
Character orbit 570.m
Rep. character $\chi_{570}(37,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $120$
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.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 736 120 616
Cusp forms 704 120 584
Eisenstein series 32 0 32

Trace form

\( 120 q - 32 q^{5} - 16 q^{7} + O(q^{10}) \) \( 120 q - 32 q^{5} - 16 q^{7} + 112 q^{11} - 1920 q^{16} - 256 q^{17} - 760 q^{23} - 304 q^{25} + 608 q^{26} - 64 q^{28} - 96 q^{30} + 688 q^{35} + 4320 q^{36} + 352 q^{38} + 80 q^{43} + 400 q^{47} - 2960 q^{55} - 1464 q^{57} + 3456 q^{61} - 64 q^{62} + 144 q^{63} - 1024 q^{68} - 2592 q^{73} - 608 q^{76} - 4072 q^{77} + 512 q^{80} - 9720 q^{81} - 1984 q^{82} - 10760 q^{83} + 1448 q^{85} + 912 q^{87} + 3040 q^{92} + 912 q^{93} - 1456 q^{95} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(570, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)