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Properties

Label 1296.3.bt
Level $1296$
Weight $3$
Character orbit 1296.bt
Rep. character $\chi_{1296}(43,\cdot)$
Character field $\Q(\zeta_{108})$
Dimension $15480$
Sturm bound $648$

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Defining parameters

Level: \( N \) \(=\) \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1296.bt (of order \(108\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1296 \)
Character field: \(\Q(\zeta_{108})\)
Sturm bound: \(648\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1296, [\chi])\).

Total New Old
Modular forms 15624 15624 0
Cusp forms 15480 15480 0
Eisenstein series 144 144 0

Trace form

\( 15480 q - 36 q^{2} - 36 q^{3} - 36 q^{4} - 36 q^{5} - 36 q^{6} - 72 q^{7} - 36 q^{8} + O(q^{10}) \) \( 15480 q - 36 q^{2} - 36 q^{3} - 36 q^{4} - 36 q^{5} - 36 q^{6} - 72 q^{7} - 36 q^{8} - 36 q^{10} - 36 q^{11} - 36 q^{12} - 36 q^{13} - 36 q^{14} - 36 q^{16} - 72 q^{17} - 36 q^{18} - 36 q^{19} - 36 q^{20} - 36 q^{21} - 36 q^{22} - 72 q^{23} - 36 q^{24} - 18 q^{26} - 36 q^{27} - 18 q^{28} - 36 q^{29} - 36 q^{30} - 36 q^{32} - 72 q^{33} - 36 q^{34} - 36 q^{35} - 36 q^{36} - 36 q^{37} - 36 q^{38} - 72 q^{39} - 36 q^{40} + 954 q^{42} - 36 q^{43} - 36 q^{44} - 36 q^{45} - 36 q^{46} - 36 q^{48} - 72 q^{49} + 666 q^{50} - 36 q^{51} - 36 q^{52} - 18 q^{53} + 216 q^{54} - 36 q^{55} - 36 q^{56} - 36 q^{58} - 36 q^{59} - 36 q^{60} - 36 q^{61} + 1746 q^{62} - 36 q^{64} - 72 q^{65} - 1908 q^{66} - 36 q^{67} - 36 q^{68} - 36 q^{69} - 36 q^{70} - 72 q^{71} - 36 q^{72} - 36 q^{74} - 36 q^{75} - 36 q^{76} - 36 q^{77} - 36 q^{78} - 72 q^{80} - 72 q^{81} - 72 q^{82} - 36 q^{83} - 36 q^{84} - 36 q^{85} - 36 q^{86} - 72 q^{87} - 36 q^{88} - 36 q^{90} - 36 q^{91} - 36 q^{92} - 36 q^{93} - 36 q^{94} - 36 q^{96} - 72 q^{97} - 36 q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1296, [\chi])\) into newform subspaces

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