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Properties

Label 539.4.j
Level $539$
Weight $4$
Character orbit 539.j
Rep. character $\chi_{539}(78,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $840$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 539.j (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(224\)

Dimensions

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

Total New Old
Modular forms 1020 840 180
Cusp forms 996 840 156
Eisenstein series 24 0 24

Trace form

\( 840 q - 560 q^{4} + 20 q^{5} - 40 q^{6} - 20 q^{7} + 84 q^{8} - 1120 q^{9} + O(q^{10}) \) \( 840 q - 560 q^{4} + 20 q^{5} - 40 q^{6} - 20 q^{7} + 84 q^{8} - 1120 q^{9} + 12 q^{10} - 598 q^{12} + 8 q^{13} - 402 q^{14} + 168 q^{15} - 2184 q^{16} + 96 q^{17} - 140 q^{18} - 232 q^{19} - 148 q^{20} - 76 q^{21} - 308 q^{24} - 3500 q^{25} + 628 q^{26} + 288 q^{27} + 128 q^{28} + 644 q^{29} + 448 q^{30} - 2024 q^{31} - 2520 q^{32} + 132 q^{33} + 732 q^{34} + 228 q^{35} - 2660 q^{36} + 2548 q^{37} + 172 q^{38} + 2520 q^{39} + 2376 q^{40} - 664 q^{41} - 2240 q^{42} - 336 q^{43} + 1540 q^{44} - 1692 q^{45} - 2380 q^{46} - 588 q^{47} + 4140 q^{48} + 292 q^{49} - 12236 q^{50} + 224 q^{51} + 3508 q^{52} - 280 q^{53} - 4756 q^{54} + 440 q^{55} + 958 q^{56} + 3528 q^{57} + 196 q^{58} + 2728 q^{59} + 1848 q^{60} + 4348 q^{61} - 464 q^{62} + 6500 q^{63} - 12012 q^{64} + 1568 q^{65} + 3278 q^{66} - 1680 q^{67} - 3092 q^{68} - 2808 q^{69} + 6324 q^{70} + 3556 q^{71} - 10570 q^{72} + 1160 q^{73} - 1680 q^{74} + 7292 q^{75} - 10062 q^{76} - 88 q^{77} + 7042 q^{78} + 392 q^{79} + 2424 q^{80} - 23632 q^{81} + 17862 q^{82} + 3204 q^{83} + 2444 q^{84} - 784 q^{85} + 5586 q^{86} - 3168 q^{87} + 6192 q^{89} + 11518 q^{90} - 4248 q^{91} + 7154 q^{92} - 11480 q^{93} - 10290 q^{94} - 5096 q^{95} - 31978 q^{96} - 8992 q^{97} + 12798 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(539, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)