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Properties

Label 2736.3.hi
Level $2736$
Weight $3$
Character orbit 2736.hi
Rep. character $\chi_{2736}(43,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $11472$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2736.hi (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2736 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2736, [\chi])\).

Total New Old
Modular forms 11568 11568 0
Cusp forms 11472 11472 0
Eisenstein series 96 96 0

Trace form

\( 11472 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{6} - 24 q^{7} - 12 q^{8} + O(q^{10}) \) \( 11472 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{6} - 24 q^{7} - 12 q^{8} - 24 q^{10} + 6 q^{11} - 6 q^{12} - 6 q^{13} - 102 q^{14} - 6 q^{16} - 48 q^{17} - 24 q^{18} - 24 q^{19} - 12 q^{20} - 120 q^{21} - 6 q^{22} - 12 q^{23} - 12 q^{24} + 132 q^{26} - 6 q^{27} - 120 q^{28} - 6 q^{29} + 288 q^{30} - 6 q^{32} - 24 q^{33} - 6 q^{34} - 174 q^{35} - 12 q^{36} - 48 q^{37} - 6 q^{38} - 48 q^{39} - 6 q^{40} - 744 q^{42} - 6 q^{43} + 174 q^{44} - 6 q^{45} - 12 q^{46} - 12 q^{48} + 78264 q^{49} + 6 q^{50} - 12 q^{51} - 6 q^{52} - 24 q^{53} - 936 q^{54} - 48 q^{55} + 282 q^{56} - 12 q^{58} - 6 q^{59} + 534 q^{60} - 6 q^{61} - 12 q^{64} + 12 q^{65} - 672 q^{66} - 6 q^{67} - 12 q^{68} - 6 q^{69} - 300 q^{70} - 48 q^{71} - 480 q^{72} - 510 q^{74} + 648 q^{75} - 6 q^{76} - 600 q^{77} + 12 q^{78} - 24 q^{80} - 24 q^{81} - 24 q^{82} - 12 q^{83} - 1182 q^{84} - 6 q^{85} - 6 q^{86} - 12 q^{87} - 12 q^{88} + 1068 q^{90} - 318 q^{91} - 6 q^{92} - 66 q^{93} - 12 q^{94} + 690 q^{96} - 12 q^{97} - 342 q^{98} - 498 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

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