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Properties

Label 570.6.k
Level $570$
Weight $6$
Character orbit 570.k
Rep. character $\chi_{570}(77,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $360$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
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 360 856
Cusp forms 1184 360 824
Eisenstein series 32 0 32

Trace form

\( 360 q + 8 q^{3} - 160 q^{6} - 152 q^{7} + O(q^{10}) \) \( 360 q + 8 q^{3} - 160 q^{6} - 152 q^{7} + 992 q^{10} - 128 q^{12} - 3184 q^{13} - 1912 q^{15} - 92160 q^{16} + 1520 q^{21} - 2848 q^{22} + 26448 q^{25} - 12976 q^{27} - 2432 q^{28} - 6816 q^{30} - 9680 q^{31} + 9632 q^{33} + 26240 q^{36} + 95168 q^{37} + 1024 q^{40} - 52896 q^{42} - 55072 q^{43} - 117760 q^{46} - 2048 q^{48} + 134400 q^{51} + 50944 q^{52} + 183160 q^{55} - 76000 q^{58} - 53888 q^{60} - 278000 q^{61} + 382096 q^{63} + 74320 q^{67} + 75936 q^{70} - 615864 q^{73} - 107072 q^{75} - 103840 q^{78} + 598120 q^{81} + 525952 q^{82} + 47520 q^{85} - 45568 q^{88} - 108384 q^{90} + 38720 q^{91} + 219304 q^{93} + 40960 q^{96} + 935144 q^{97} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(570, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)