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Properties

Label 531.5.h
Level $531$
Weight $5$
Character orbit 531.h
Rep. character $\chi_{531}(119,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $464$
Sturm bound $300$

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Defining parameters

Level: \( N \) \(=\) \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 531.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(300\)

Dimensions

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

Total New Old
Modular forms 484 464 20
Cusp forms 476 464 12
Eisenstein series 8 0 8

Trace form

\( 464 q + 1856 q^{4} + 128 q^{6} - 26 q^{7} - 104 q^{9} + O(q^{10}) \) \( 464 q + 1856 q^{4} + 128 q^{6} - 26 q^{7} - 104 q^{9} - 468 q^{11} + 10 q^{13} + 576 q^{14} - 13 q^{15} - 14848 q^{16} - 1492 q^{18} - 308 q^{19} - 3906 q^{20} - 1558 q^{21} + 678 q^{24} + 29000 q^{25} - 1731 q^{27} - 1664 q^{28} + 2106 q^{29} + 690 q^{30} - 1472 q^{31} + 9900 q^{32} + 1042 q^{33} - 804 q^{34} - 5604 q^{36} + 2068 q^{37} - 3420 q^{38} - 4826 q^{39} + 3300 q^{40} - 8928 q^{41} - 11954 q^{42} + 1408 q^{43} + 13151 q^{45} + 11448 q^{46} + 26050 q^{48} - 73794 q^{49} - 18432 q^{50} - 7300 q^{51} - 320 q^{52} + 11886 q^{54} + 13824 q^{56} - 3936 q^{57} + 2980 q^{60} - 7262 q^{61} + 2188 q^{63} - 239416 q^{64} - 26298 q^{65} + 24414 q^{66} + 7630 q^{67} + 8118 q^{68} + 20280 q^{69} + 4800 q^{70} - 11146 q^{72} + 19012 q^{73} - 83538 q^{74} - 47286 q^{75} - 2276 q^{76} - 24336 q^{77} - 41914 q^{78} - 2570 q^{79} - 55296 q^{81} - 15360 q^{82} + 19566 q^{83} + 2940 q^{84} - 23484 q^{85} + 47700 q^{86} - 27295 q^{87} - 10880 q^{90} - 60076 q^{91} - 96750 q^{92} + 4286 q^{93} + 1344 q^{94} - 9504 q^{95} + 62912 q^{96} + 31306 q^{97} - 44684 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{5}^{\mathrm{old}}(531, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(531, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)