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Properties

Label 539.4.s
Level $539$
Weight $4$
Character orbit 539.s
Rep. character $\chi_{539}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $928$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 539.s (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(224\)

Dimensions

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

Total New Old
Modular forms 1408 992 416
Cusp forms 1280 928 352
Eisenstein series 128 64 64

Trace form

\( 928 q + 5 q^{2} + 9 q^{3} - 425 q^{4} - 15 q^{5} + 120 q^{8} - 1065 q^{9} + O(q^{10}) \) \( 928 q + 5 q^{2} + 9 q^{3} - 425 q^{4} - 15 q^{5} + 120 q^{8} - 1065 q^{9} + 32 q^{11} - 24 q^{12} - 120 q^{15} + 1595 q^{16} + 45 q^{17} + 455 q^{18} + 15 q^{19} - 1408 q^{22} - 180 q^{23} + 1365 q^{24} - 2645 q^{25} + 57 q^{26} + 660 q^{29} + 545 q^{30} - 1233 q^{31} + 1614 q^{33} - 3402 q^{36} + 375 q^{37} + 135 q^{38} - 1835 q^{39} - 2145 q^{40} + 1447 q^{44} - 2610 q^{45} - 2425 q^{46} - 447 q^{47} - 1290 q^{50} - 195 q^{51} + 15 q^{52} + 851 q^{53} - 600 q^{57} - 995 q^{58} + 477 q^{59} - 341 q^{60} + 2475 q^{61} + 13072 q^{64} + 1695 q^{66} + 5104 q^{67} - 465 q^{68} + 632 q^{71} + 3215 q^{72} - 2865 q^{73} - 1885 q^{74} - 2313 q^{75} - 10996 q^{78} - 2545 q^{79} - 9495 q^{80} + 233 q^{81} - 7959 q^{82} + 23280 q^{85} + 9173 q^{86} + 847 q^{88} - 1536 q^{89} - 1120 q^{92} - 6033 q^{93} + 18615 q^{94} + 8215 q^{95} - 7635 q^{96} - 18136 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{4}^{\mathrm{old}}(539, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(539, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)