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Properties

Label 225.6.u
Level $225$
Weight $6$
Character orbit 225.u
Rep. character $\chi_{225}(4,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1184$
Sturm bound $180$

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Defining parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 225.u (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(180\)

Dimensions

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

Total New Old
Modular forms 1216 1216 0
Cusp forms 1184 1184 0
Eisenstein series 32 32 0

Trace form

\( 1184 q - 5 q^{2} - 10 q^{3} - 2339 q^{4} - 120 q^{5} + 58 q^{6} - 20 q^{8} - 68 q^{9} + O(q^{10}) \) \( 1184 q - 5 q^{2} - 10 q^{3} - 2339 q^{4} - 120 q^{5} + 58 q^{6} - 20 q^{8} - 68 q^{9} + 48 q^{10} + 965 q^{11} - 330 q^{12} - 5 q^{13} - 1763 q^{14} + 1758 q^{15} + 36285 q^{16} - 20 q^{17} - 12 q^{19} - 3527 q^{20} + 5373 q^{21} - 5 q^{22} - 5 q^{23} + 5414 q^{24} - 6616 q^{25} + 64992 q^{26} + 12575 q^{27} - 10260 q^{28} - 10095 q^{29} - 22588 q^{30} + 4431 q^{31} - 24785 q^{33} - 67 q^{34} - 14926 q^{35} + 13284 q^{36} - 20 q^{37} + 86025 q^{38} - 17248 q^{39} - 2041 q^{40} + 26893 q^{41} + 162010 q^{42} + 73460 q^{44} - 90420 q^{45} + 116 q^{46} + 25520 q^{47} + 166215 q^{48} + 1306136 q^{49} + 26461 q^{50} - 39366 q^{51} - 165 q^{52} - 20 q^{53} - 98609 q^{54} - 21044 q^{55} + 121522 q^{56} - 5 q^{58} - 126390 q^{59} + 262591 q^{60} - 3 q^{61} - 132260 q^{62} - 83700 q^{63} + 1093428 q^{64} - 211245 q^{65} - 99322 q^{66} - 13790 q^{67} + 55366 q^{69} + 167598 q^{70} - 485746 q^{71} + 298390 q^{72} - 20 q^{73} + 524122 q^{74} + 354523 q^{75} + 2168 q^{76} - 325315 q^{77} - 818290 q^{78} + 89505 q^{79} - 1439062 q^{80} - 509988 q^{81} - 470335 q^{83} - 257163 q^{84} - 43941 q^{85} + 148305 q^{86} + 454615 q^{87} - 5 q^{88} + 620126 q^{89} + 76621 q^{90} - 100854 q^{91} + 327995 q^{92} + 86921 q^{94} + 380023 q^{95} + 358663 q^{96} - 5 q^{97} - 167770 q^{98} - 677040 q^{99} + O(q^{100}) \)

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.