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Properties

Label 1053.2.cn
Level $1053$
Weight $2$
Character orbit 1053.cn
Rep. character $\chi_{1053}(2,\cdot)$
Character field $\Q(\zeta_{108})$
Dimension $4464$
Sturm bound $252$

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Defining parameters

Level: \( N \) \(=\) \( 1053 = 3^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1053.cn (of order \(108\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1053 \)
Character field: \(\Q(\zeta_{108})\)
Sturm bound: \(252\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1053, [\chi])\).

Total New Old
Modular forms 4608 4608 0
Cusp forms 4464 4464 0
Eisenstein series 144 144 0

Trace form

\( 4464 q - 36 q^{2} - 18 q^{3} - 54 q^{4} - 36 q^{5} - 36 q^{6} - 36 q^{7} - 36 q^{8} - 18 q^{9} + O(q^{10}) \) \( 4464 q - 36 q^{2} - 18 q^{3} - 54 q^{4} - 36 q^{5} - 36 q^{6} - 36 q^{7} - 36 q^{8} - 18 q^{9} - 54 q^{10} - 36 q^{11} - 36 q^{13} - 72 q^{14} - 36 q^{15} - 18 q^{16} - 54 q^{17} - 36 q^{18} - 36 q^{19} - 36 q^{20} - 36 q^{21} - 18 q^{22} - 54 q^{23} - 252 q^{24} - 54 q^{26} - 18 q^{27} - 18 q^{28} - 18 q^{29} - 54 q^{30} - 36 q^{31} - 144 q^{32} - 36 q^{33} - 36 q^{34} - 18 q^{35} - 54 q^{36} - 36 q^{37} - 36 q^{39} - 72 q^{40} - 36 q^{41} - 18 q^{42} - 54 q^{43} + 252 q^{44} + 72 q^{45} - 36 q^{46} + 72 q^{47} - 18 q^{48} - 54 q^{49} - 270 q^{50} - 36 q^{52} - 108 q^{53} - 36 q^{54} - 36 q^{55} - 54 q^{56} - 144 q^{57} - 36 q^{58} - 36 q^{59} - 504 q^{60} - 18 q^{61} - 54 q^{62} + 180 q^{63} - 144 q^{65} + 72 q^{66} - 36 q^{67} - 18 q^{68} - 54 q^{69} - 36 q^{70} - 36 q^{71} + 396 q^{72} - 36 q^{73} - 162 q^{74} - 54 q^{75} - 36 q^{76} + 72 q^{78} - 180 q^{79} - 18 q^{81} - 108 q^{82} - 36 q^{83} + 18 q^{84} - 144 q^{85} - 180 q^{86} - 162 q^{87} - 54 q^{88} - 36 q^{89} - 36 q^{91} + 180 q^{92} - 36 q^{93} - 18 q^{94} - 54 q^{95} - 270 q^{96} - 36 q^{97} - 576 q^{98} - 72 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1053, [\chi])\) into newform subspaces

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