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Properties

Label 2268.2.dh
Level $2268$
Weight $2$
Character orbit 2268.dh
Rep. character $\chi_{2268}(103,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $7704$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.dh (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2268 \)
Character field: \(\Q(\zeta_{54})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2268, [\chi])\).

Total New Old
Modular forms 7848 7848 0
Cusp forms 7704 7704 0
Eisenstein series 144 144 0

Trace form

\( 7704 q - 9 q^{2} - 9 q^{4} - 54 q^{5} - 36 q^{8} - 18 q^{9} + O(q^{10}) \) \( 7704 q - 9 q^{2} - 9 q^{4} - 54 q^{5} - 36 q^{8} - 18 q^{9} - 27 q^{10} - 27 q^{12} - 18 q^{14} - 9 q^{16} - 54 q^{17} - 9 q^{18} - 36 q^{21} - 36 q^{22} - 27 q^{24} - 18 q^{25} - 9 q^{28} - 72 q^{29} - 9 q^{30} - 9 q^{32} - 54 q^{33} - 36 q^{36} - 18 q^{37} - 27 q^{38} - 27 q^{40} - 108 q^{42} - 9 q^{44} - 54 q^{45} - 9 q^{46} + 297 q^{48} - 36 q^{49} - 36 q^{50} - 27 q^{52} - 36 q^{53} - 27 q^{54} + 108 q^{56} - 72 q^{57} - 9 q^{58} - 9 q^{60} - 54 q^{61} - 297 q^{62} - 36 q^{64} - 18 q^{65} - 27 q^{66} + 108 q^{68} - 18 q^{70} - 9 q^{72} - 54 q^{73} - 9 q^{74} - 36 q^{77} - 63 q^{78} - 54 q^{80} - 18 q^{81} - 54 q^{82} - 72 q^{84} - 72 q^{85} - 9 q^{86} - 9 q^{88} - 54 q^{89} - 126 q^{92} - 18 q^{93} - 27 q^{94} - 27 q^{96} - 189 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2268, [\chi])\) into newform subspaces

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