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Properties

Label 2493.2.g
Level $2493$
Weight $2$
Character orbit 2493.g
Rep. character $\chi_{2493}(160,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $552$
Sturm bound $556$

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Defining parameters

Level: \( N \) \(=\) \( 2493 = 3^{2} \cdot 277 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2493.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2493 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(556\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2493, [\chi])\).

Total New Old
Modular forms 560 560 0
Cusp forms 552 552 0
Eisenstein series 8 8 0

Trace form

\( 552 q - 2 q^{2} - q^{3} - 276 q^{4} - 2 q^{5} + 3 q^{6} - 6 q^{8} - q^{9} + O(q^{10}) \) \( 552 q - 2 q^{2} - q^{3} - 276 q^{4} - 2 q^{5} + 3 q^{6} - 6 q^{8} - q^{9} + q^{11} - 5 q^{12} - 3 q^{13} + 26 q^{14} - 10 q^{15} - 276 q^{16} + q^{17} - 12 q^{19} + 2 q^{20} - 22 q^{21} + 6 q^{22} - 14 q^{23} - 16 q^{24} + 534 q^{25} + 12 q^{26} - 16 q^{27} - 26 q^{29} + 9 q^{30} + 9 q^{31} + 24 q^{32} - 12 q^{33} + 3 q^{34} - 13 q^{35} + 5 q^{36} - 6 q^{37} - 14 q^{38} - 10 q^{39} - 12 q^{40} + 12 q^{41} + 17 q^{42} - 3 q^{43} + 4 q^{44} + 16 q^{45} - 42 q^{47} + 56 q^{48} - 264 q^{49} + 8 q^{50} + 8 q^{51} - 12 q^{52} + 10 q^{53} + 37 q^{54} - 12 q^{55} - 46 q^{56} + 5 q^{57} + 6 q^{58} + 2 q^{59} - 16 q^{60} + 12 q^{61} + 19 q^{62} + 31 q^{63} + 522 q^{64} - 21 q^{65} - 63 q^{66} - 30 q^{67} + 16 q^{68} - 23 q^{69} - 18 q^{70} + 20 q^{71} - 35 q^{72} + 6 q^{73} + 91 q^{74} + 23 q^{75} + 6 q^{76} + 39 q^{77} + 14 q^{78} + 26 q^{80} + 19 q^{81} - 12 q^{82} - 30 q^{83} + 60 q^{84} - 21 q^{85} - 34 q^{86} + 56 q^{87} + 27 q^{88} + 32 q^{89} - 51 q^{90} + 6 q^{91} - 33 q^{92} + 26 q^{93} + 30 q^{94} + 40 q^{95} + 53 q^{96} - 48 q^{97} + 75 q^{98} + 20 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2493, [\chi])\) into newform subspaces

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