Properties

Label 225.6.k
Level $225$
Weight $6$
Character orbit 225.k
Rep. character $\chi_{225}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $176$
Sturm bound $180$

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Defining parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 225.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(180\)

Dimensions

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

Total New Old
Modular forms 312 184 128
Cusp forms 288 176 112
Eisenstein series 24 8 16

Trace form

\( 176q + 1378q^{4} - 100q^{6} - 878q^{9} + O(q^{10}) \) \( 176q + 1378q^{4} - 100q^{6} - 878q^{9} + 586q^{11} - 1614q^{14} - 21058q^{16} + 8q^{19} + 3090q^{21} + 11490q^{24} - 17864q^{26} + 4690q^{29} + 4432q^{31} + 12726q^{34} - 46448q^{36} + 7670q^{39} + 50954q^{41} + 165064q^{44} - 91680q^{46} + 178818q^{49} - 75034q^{51} - 217802q^{54} + 89580q^{56} - 133270q^{59} - 46742q^{61} - 502544q^{64} - 90446q^{66} + 80214q^{69} + 31328q^{71} - 336740q^{74} + 48418q^{76} + 17450q^{79} + 252614q^{81} + 287550q^{84} + 158086q^{86} + 102876q^{89} + 131900q^{91} + 38250q^{94} + 352900q^{96} - 795910q^{99} + O(q^{100}) \)

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

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

Decomposition of \(S_{6}^{\mathrm{old}}(225, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(225, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)