↑

Properties

Label 720.6.z
Level $720$
Weight $6$
Character orbit 720.z
Rep. character $\chi_{720}(163,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $596$
Sturm bound $864$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 720.z (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(720, [\chi])\).

Total New Old
Modular forms 1456 604 852
Cusp forms 1424 596 828
Eisenstein series 32 8 24

Trace form

\( 596 q + 2 q^{2} - 20 q^{4} + 2 q^{5} - 4 q^{7} - 244 q^{8} + O(q^{10}) \) \( 596 q + 2 q^{2} - 20 q^{4} + 2 q^{5} - 4 q^{7} - 244 q^{8} + 62 q^{10} + 4 q^{11} + 1216 q^{16} + 4 q^{17} - 2360 q^{19} + 836 q^{20} + 2436 q^{22} + 4 q^{23} + 884 q^{26} - 5924 q^{28} - 17608 q^{32} + 4080 q^{34} - 8636 q^{35} + 22032 q^{38} - 43048 q^{40} - 78440 q^{44} - 17964 q^{46} - 65256 q^{47} + 24198 q^{50} - 11240 q^{52} + 4 q^{53} - 4 q^{55} - 64676 q^{56} - 86232 q^{58} + 14480 q^{59} - 48084 q^{61} + 128820 q^{62} - 35960 q^{64} + 4 q^{65} - 162256 q^{68} + 36260 q^{70} - 143832 q^{71} + 10072 q^{73} - 250668 q^{74} - 94444 q^{76} + 67232 q^{77} - 231776 q^{80} - 136760 q^{82} + 126444 q^{83} + 6248 q^{85} - 85316 q^{86} + 330992 q^{88} - 164724 q^{91} - 128252 q^{92} - 106060 q^{94} - 204760 q^{95} - 4 q^{97} - 538554 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(720, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(720, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(720, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)