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Properties

Label 570.6.m
Level $570$
Weight $6$
Character orbit 570.m
Rep. character $\chi_{570}(37,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $200$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 570.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(i)\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(570, [\chi])\).

Total New Old
Modular forms 1216 200 1016
Cusp forms 1184 200 984
Eisenstein series 32 0 32

Trace form

\( 200 q + 88 q^{5} + 472 q^{7} + O(q^{10}) \) \( 200 q + 88 q^{5} + 472 q^{7} - 80 q^{11} - 51200 q^{16} - 1528 q^{17} + 12200 q^{23} - 3784 q^{25} - 3520 q^{26} + 7552 q^{28} + 16704 q^{30} + 25288 q^{35} + 259200 q^{36} + 1984 q^{38} - 141080 q^{43} - 108680 q^{47} + 50000 q^{55} + 33768 q^{57} + 43360 q^{61} + 126848 q^{62} - 38232 q^{63} - 24448 q^{68} + 399576 q^{73} + 27520 q^{76} - 332656 q^{77} - 22528 q^{80} - 1312200 q^{81} + 254848 q^{82} + 774040 q^{83} + 841688 q^{85} - 148464 q^{87} - 195200 q^{92} + 1584 q^{93} + 346664 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(570, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(570, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(570, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)