↑

Properties

Label 539.4.p
Level $539$
Weight $4$
Character orbit 539.p
Rep. character $\chi_{539}(76,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $996$
Sturm bound $224$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 539.p (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(539, [\chi])\).

Total New Old
Modular forms 1020 1020 0
Cusp forms 996 996 0
Eisenstein series 24 24 0

Trace form

\( 996 q - 14 q^{3} + 646 q^{4} - 14 q^{5} + 1448 q^{9} + O(q^{10}) \) \( 996 q - 14 q^{3} + 646 q^{4} - 14 q^{5} + 1448 q^{9} - 103 q^{11} - 14 q^{12} - 8 q^{14} + 302 q^{15} - 2546 q^{16} + 882 q^{20} - 245 q^{22} + 298 q^{23} + 4668 q^{25} - 1078 q^{26} + 70 q^{27} - 7 q^{33} + 1302 q^{34} - 6098 q^{36} + 158 q^{37} - 1862 q^{38} - 2298 q^{42} - 1951 q^{44} + 434 q^{45} + 714 q^{47} + 2420 q^{49} - 1522 q^{53} - 2527 q^{55} + 2418 q^{56} - 4242 q^{58} + 3822 q^{59} - 9358 q^{60} + 5518 q^{64} + 1659 q^{66} + 1040 q^{67} - 10934 q^{69} - 5010 q^{70} - 570 q^{71} - 14 q^{75} + 15 q^{77} - 756 q^{78} - 7060 q^{81} - 14 q^{82} + 1932 q^{86} - 7973 q^{88} + 9226 q^{89} + 22294 q^{91} - 1690 q^{92} + 3620 q^{93} - 9556 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(539, [\chi])\) into newform subspaces

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