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Properties

Label 539.4.v
Level $539$
Weight $4$
Character orbit 539.v
Rep. character $\chi_{539}(15,\cdot)$
Character field $\Q(\zeta_{35})$
Dimension $3984$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 539.v (of order \(35\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{35})\)
Sturm bound: \(224\)

Dimensions

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

Total New Old
Modular forms 4080 4080 0
Cusp forms 3984 3984 0
Eisenstein series 96 96 0

Trace form

\( 3984 q - 15 q^{2} - 15 q^{3} + 641 q^{4} + q^{5} - 23 q^{6} - 47 q^{8} + 1443 q^{9} + O(q^{10}) \) \( 3984 q - 15 q^{2} - 15 q^{3} + 641 q^{4} + q^{5} - 23 q^{6} - 47 q^{8} + 1443 q^{9} - 280 q^{10} + 78 q^{11} - 180 q^{12} + 37 q^{13} + 70 q^{14} - 753 q^{15} + 2569 q^{16} - 371 q^{17} + 48 q^{18} - 1084 q^{19} - 903 q^{20} + 58 q^{21} - 680 q^{22} - 348 q^{23} + 1307 q^{24} + 4215 q^{25} + 769 q^{26} - 33 q^{27} - 658 q^{28} + 405 q^{29} - 406 q^{30} + 792 q^{31} - 328 q^{32} - 1734 q^{33} - 5152 q^{34} + 1282 q^{35} + 6287 q^{36} + 489 q^{37} + 1885 q^{38} + 157 q^{39} - 1843 q^{40} + 221 q^{41} - 4615 q^{42} + 800 q^{43} + 1558 q^{44} - 4568 q^{45} - 751 q^{46} - 1053 q^{47} - 2194 q^{48} - 3888 q^{49} + 1130 q^{50} + 1557 q^{51} - 1335 q^{52} + 4465 q^{53} - 934 q^{54} + 454 q^{55} - 4362 q^{56} + 1711 q^{57} + 5833 q^{58} + 4453 q^{59} + 14137 q^{60} + 2013 q^{61} - 2407 q^{62} - 583 q^{63} + 1329 q^{64} + 2484 q^{65} + 1592 q^{66} - 3904 q^{67} - 4160 q^{68} - 9045 q^{69} - 6933 q^{70} - 1135 q^{71} - 6455 q^{72} + 6917 q^{73} + 4657 q^{74} - 5431 q^{75} - 5848 q^{76} + 1259 q^{77} - 22324 q^{78} - 2640 q^{79} - 3958 q^{80} - 1161 q^{81} + 2113 q^{82} - 3143 q^{83} + 9457 q^{84} + 3965 q^{85} - 4636 q^{86} + 4624 q^{87} - 6228 q^{88} + 3272 q^{89} + 10223 q^{90} + 7320 q^{91} + 2668 q^{92} + 4791 q^{93} + 18041 q^{94} - 4001 q^{95} + 3799 q^{96} - 4908 q^{97} - 5722 q^{98} + 36212 q^{99} + O(q^{100}) \)

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.