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Properties

Label 539.4.bf
Level $539$
Weight $4$
Character orbit 539.bf
Rep. character $\chi_{539}(17,\cdot)$
Character field $\Q(\zeta_{210})$
Dimension $7968$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 539.bf (of order \(210\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{210})\)
Sturm bound: \(224\)

Dimensions

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

Total New Old
Modular forms 8160 8160 0
Cusp forms 7968 7968 0
Eisenstein series 192 192 0

Trace form

\( 7968 q - 65 q^{2} - 33 q^{3} + 617 q^{4} - 57 q^{5} - 70 q^{6} - 70 q^{7} - 50 q^{8} + 1419 q^{9} + O(q^{10}) \) \( 7968 q - 65 q^{2} - 33 q^{3} + 617 q^{4} - 57 q^{5} - 70 q^{6} - 70 q^{7} - 50 q^{8} + 1419 q^{9} - 150 q^{11} - 136 q^{12} - 70 q^{13} - 208 q^{14} - 768 q^{15} - 2611 q^{16} - 1145 q^{17} - 30 q^{18} - 90 q^{19} + 854 q^{20} - 1540 q^{22} + 624 q^{23} - 1855 q^{24} + 3547 q^{25} - 1049 q^{26} - 168 q^{27} - 420 q^{28} + 650 q^{29} - 300 q^{30} - 1296 q^{31} + 1558 q^{33} - 5376 q^{34} - 1870 q^{35} + 11000 q^{36} - 123 q^{37} + 3453 q^{38} - 65 q^{39} + 7865 q^{40} - 70 q^{41} - 1202 q^{42} + 1757 q^{44} + 5286 q^{45} - 145 q^{46} - 1903 q^{47} - 3784 q^{49} - 1370 q^{50} - 10985 q^{51} - 55 q^{52} + 2425 q^{53} - 1946 q^{55} - 5920 q^{56} - 610 q^{57} + 10225 q^{58} + 4271 q^{59} + 26229 q^{60} + 2405 q^{61} + 18690 q^{62} + 175 q^{63} - 16046 q^{64} + 3305 q^{66} + 2080 q^{67} - 570 q^{68} - 10962 q^{69} + 3043 q^{70} + 2210 q^{71} - 4505 q^{72} + 3785 q^{73} - 1955 q^{74} - 2355 q^{75} - 551 q^{77} + 19332 q^{78} - 1080 q^{79} - 9558 q^{80} + 13821 q^{81} - 8001 q^{82} - 70 q^{83} + 4075 q^{84} + 4150 q^{85} - 644 q^{86} + 15458 q^{88} + 3392 q^{89} - 70 q^{90} - 3138 q^{91} - 7194 q^{92} + 1491 q^{93} - 27655 q^{94} + 1265 q^{95} - 7705 q^{96} + 37400 q^{99} + O(q^{100}) \)

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.