↑

Properties

Label 531.5.k
Level $531$
Weight $5$
Character orbit 531.k
Rep. character $\chi_{531}(10,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $2772$
Sturm bound $300$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 531.k (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q(\zeta_{58})\)
Sturm bound: \(300\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(531, [\chi])\).

Total New Old
Modular forms 6832 2828 4004
Cusp forms 6608 2772 3836
Eisenstein series 224 56 168

Trace form

\( 2772 q + 29 q^{2} + 757 q^{4} + 33 q^{5} - 107 q^{7} + 29 q^{8} + O(q^{10}) \) \( 2772 q + 29 q^{2} + 757 q^{4} + 33 q^{5} - 107 q^{7} + 29 q^{8} - 29 q^{10} + 29 q^{11} - 29 q^{13} + 29 q^{14} - 5931 q^{16} - 534 q^{17} + 603 q^{19} - 423 q^{20} - 1459 q^{22} + 29 q^{23} - 10012 q^{25} + 899 q^{26} + 1433 q^{28} - 471 q^{29} - 29 q^{31} + 29 q^{32} - 29 q^{34} + 6064 q^{35} - 29 q^{37} + 29 q^{38} - 29 q^{40} - 405 q^{41} - 29 q^{43} + 29 q^{44} + 32119 q^{46} + 8642 q^{47} - 40320 q^{49} - 33379 q^{50} - 47357 q^{52} - 35205 q^{53} - 26390 q^{55} - 50083 q^{56} - 3008 q^{59} + 19633 q^{61} + 41825 q^{62} + 180569 q^{64} + 49358 q^{65} + 27637 q^{67} + 64155 q^{68} - 5597 q^{70} - 23568 q^{71} - 34394 q^{73} - 99685 q^{74} - 11253 q^{76} + 29 q^{77} - 10863 q^{79} + 26877 q^{80} - 29 q^{82} + 29 q^{83} - 9673 q^{85} - 58837 q^{86} + 13697 q^{88} + 29 q^{89} - 29 q^{91} + 29 q^{92} + 35019 q^{94} + 12751 q^{95} - 29 q^{97} + 272774 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(531, [\chi])\) into newform subspaces

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

Decomposition of \(S_{5}^{\mathrm{old}}(531, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(531, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)