↑

Properties

Label 720.4.bd
Level $720$
Weight $4$
Character orbit 720.bd
Rep. character $\chi_{720}(307,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $356$
Sturm bound $576$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 720.bd (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(720, [\chi])\).

Total New Old
Modular forms 880 364 516
Cusp forms 848 356 492
Eisenstein series 32 8 24

Trace form

\( 356 q + 2 q^{2} - 12 q^{4} + 2 q^{5} - 4 q^{7} + 44 q^{8} + O(q^{10}) \) \( 356 q + 2 q^{2} - 12 q^{4} + 2 q^{5} - 4 q^{7} + 44 q^{8} - 18 q^{10} + 4 q^{11} - 4 q^{13} + 128 q^{16} + 4 q^{17} + 24 q^{19} + 176 q^{20} - 72 q^{22} + 4 q^{23} - 268 q^{26} - 624 q^{28} - 288 q^{32} - 112 q^{34} + 24 q^{35} - 4 q^{37} - 604 q^{38} + 1872 q^{40} - 868 q^{43} - 1624 q^{44} + 20 q^{46} - 408 q^{47} + 698 q^{50} - 352 q^{52} - 4 q^{55} - 164 q^{56} - 2684 q^{58} + 688 q^{59} + 908 q^{61} + 740 q^{62} - 456 q^{64} + 4 q^{65} + 1844 q^{67} - 2680 q^{68} + 440 q^{70} - 216 q^{71} - 296 q^{73} - 1332 q^{74} + 1812 q^{76} + 3064 q^{80} + 1588 q^{82} - 252 q^{85} - 1028 q^{86} + 1312 q^{88} + 844 q^{91} + 2752 q^{92} - 1716 q^{94} + 1240 q^{95} - 4 q^{97} - 4854 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(720, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(720, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(720, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)