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Properties

Label 531.5.n
Level $531$
Weight $5$
Character orbit 531.n
Rep. character $\chi_{531}(5,\cdot)$
Character field $\Q(\zeta_{174})$
Dimension $13328$
Sturm bound $300$

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Defining parameters

Level: \( N \) \(=\) \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 531.n (of order \(174\) and degree \(56\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 531 \)
Character field: \(\Q(\zeta_{174})\)
Sturm bound: \(300\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(531, [\chi])\).

Total New Old
Modular forms 13552 13552 0
Cusp forms 13328 13328 0
Eisenstein series 224 224 0

Trace form

\( 13328 q - 81 q^{2} - 52 q^{3} - 1915 q^{4} - 63 q^{5} + 12 q^{6} - 27 q^{7} - 152 q^{9} + O(q^{10}) \) \( 13328 q - 81 q^{2} - 52 q^{3} - 1915 q^{4} - 63 q^{5} + 12 q^{6} - 27 q^{7} - 152 q^{9} - 44 q^{10} - 585 q^{11} - 718 q^{12} - 27 q^{13} + 1629 q^{14} + 2007 q^{15} + 14789 q^{16} - 1374 q^{18} + 708 q^{19} + 591 q^{20} + 540 q^{21} + 709 q^{22} + 477 q^{23} + 2162 q^{24} - 28483 q^{25} + 1565 q^{27} - 1068 q^{28} - 81 q^{29} + 1808 q^{30} - 1137 q^{31} - 7665 q^{32} - 1658 q^{33} - 251 q^{34} + 10316 q^{36} - 2208 q^{37} + 4911 q^{38} + 820 q^{39} - 701 q^{40} - 6417 q^{41} - 7328 q^{42} - 867 q^{43} + 24998 q^{45} - 44 q^{46} + 19197 q^{47} - 5606 q^{48} + 77491 q^{49} + 12291 q^{50} + 88400 q^{51} + 771 q^{52} - 85838 q^{54} - 4148 q^{55} - 12987 q^{56} - 23241 q^{57} - 12982 q^{58} - 6312 q^{59} - 179508 q^{60} - 27 q^{61} + 86135 q^{63} + 208400 q^{64} + 40527 q^{65} + 113428 q^{66} + 2451 q^{67} + 12801 q^{68} - 35966 q^{69} + 14539 q^{70} - 132486 q^{72} + 10116 q^{73} + 30543 q^{74} - 63341 q^{75} + 10341 q^{76} + 19089 q^{77} + 65976 q^{78} - 6987 q^{79} + 18464 q^{81} + 34648 q^{82} - 15921 q^{83} + 9974 q^{84} - 1277 q^{85} + 27675 q^{86} + 70365 q^{87} - 29603 q^{88} - 30758 q^{90} - 9712 q^{91} + 29391 q^{92} - 42852 q^{93} + 24043 q^{94} + 36141 q^{95} - 55626 q^{96} + 26583 q^{97} + 62878 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(531, [\chi])\) into newform subspaces

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