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Properties

Label 531.8.f
Level $531$
Weight $8$
Character orbit 531.f
Rep. character $\chi_{531}(176,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $836$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 531.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 531 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(531, [\chi])\).

Total New Old
Modular forms 844 844 0
Cusp forms 836 836 0
Eisenstein series 8 8 0

Trace form

\( 836 q - 4 q^{3} - 26626 q^{4} - 432 q^{5} - 2 q^{7} + 1192 q^{9} + O(q^{10}) \) \( 836 q - 4 q^{3} - 26626 q^{4} - 432 q^{5} - 2 q^{7} + 1192 q^{9} - 45280 q^{12} + 42507 q^{15} - 1687810 q^{16} - 4196 q^{19} + 109818 q^{20} + 3350 q^{21} + 71022 q^{22} + 6478242 q^{25} - 1087897 q^{27} + 66040 q^{28} - 6 q^{29} + 1821306 q^{36} - 3299796 q^{41} - 1305685 q^{45} + 504 q^{46} + 7046084 q^{48} - 47765496 q^{49} + 3942992 q^{51} + 11389044 q^{57} - 4952076 q^{59} - 16507684 q^{60} + 7228640 q^{63} + 222369116 q^{64} - 775274 q^{66} + 2571444 q^{68} + 3577050 q^{74} - 7679014 q^{75} + 369790 q^{76} + 1533226 q^{78} + 3618730 q^{79} + 407712 q^{81} + 26395004 q^{84} + 156248 q^{85} + 43475430 q^{86} - 12986887 q^{87} - 5841450 q^{88} - 13619412 q^{94} + 28690320 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(531, [\chi])\) into newform subspaces

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