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Properties

Label 225.6.w
Level $225$
Weight $6$
Character orbit 225.w
Rep. character $\chi_{225}(2,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $2368$
Sturm bound $180$

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Defining parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 225.w (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(180\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(225, [\chi])\).

Total New Old
Modular forms 2432 2432 0
Cusp forms 2368 2368 0
Eisenstein series 64 64 0

Trace form

\( 2368 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} + O(q^{10}) \) \( 2368 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} + 406 q^{12} - 8 q^{13} - 30 q^{14} - 3014 q^{15} - 72710 q^{16} - 5396 q^{18} - 40 q^{19} + 11112 q^{20} - 12 q^{21} + 120 q^{22} + 15792 q^{23} + 13216 q^{25} - 4358 q^{27} + 3936 q^{28} - 30 q^{29} - 3170 q^{30} - 6 q^{31} - 8340 q^{32} + 28252 q^{33} - 10 q^{34} + 4084 q^{36} + 19996 q^{37} - 49320 q^{38} + 7140 q^{39} - 2056 q^{40} - 18 q^{41} - 323046 q^{42} - 8 q^{43} + 25796 q^{45} - 24 q^{46} - 32778 q^{47} - 237100 q^{48} - 77016 q^{50} - 32 q^{51} + 4344 q^{52} + 66150 q^{54} + 40056 q^{55} - 18 q^{56} + 175046 q^{57} + 9896 q^{58} + 428400 q^{59} - 396758 q^{60} - 6 q^{61} - 442366 q^{63} - 40 q^{64} + 107904 q^{65} + 31092 q^{66} + 5506 q^{67} - 403992 q^{68} + 14750 q^{69} - 12508 q^{70} + 802122 q^{72} - 32 q^{73} + 38418 q^{75} - 4112 q^{76} + 437976 q^{77} - 180178 q^{78} - 10 q^{79} + 58888 q^{81} - 276192 q^{82} - 46764 q^{83} - 977300 q^{84} - 81632 q^{85} - 18 q^{86} - 202872 q^{87} - 240928 q^{88} + 461026 q^{90} - 24 q^{91} + 1450290 q^{92} + 1137068 q^{93} - 289330 q^{94} - 15114 q^{95} - 37260 q^{96} + 69862 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(225, [\chi])\) into newform subspaces

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