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Properties

Label 2493.2.bt
Level $2493$
Weight $2$
Character orbit 2493.bt
Rep. character $\chi_{2493}(7,\cdot)$
Character field $\Q(\zeta_{138})$
Dimension $12144$
Sturm bound $556$

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Defining parameters

Level: \( N \) \(=\) \( 2493 = 3^{2} \cdot 277 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2493.bt (of order \(138\) and degree \(44\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2493 \)
Character field: \(\Q(\zeta_{138})\)
Sturm bound: \(556\)

Dimensions

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

Total New Old
Modular forms 12320 12320 0
Cusp forms 12144 12144 0
Eisenstein series 176 176 0

Trace form

\( 12144 q - 23 q^{2} - 45 q^{3} - 295 q^{4} - 23 q^{5} - 37 q^{6} - 25 q^{7} - 92 q^{8} - 45 q^{9} + O(q^{10}) \) \( 12144 q - 23 q^{2} - 45 q^{3} - 295 q^{4} - 23 q^{5} - 37 q^{6} - 25 q^{7} - 92 q^{8} - 45 q^{9} - 88 q^{10} - 20 q^{11} - 55 q^{12} - 20 q^{13} - 23 q^{14} - 46 q^{15} + 245 q^{16} - 95 q^{17} - 58 q^{18} - 80 q^{19} - 29 q^{20} - 123 q^{21} - 13 q^{22} - 33 q^{23} - 183 q^{24} + 515 q^{25} - 92 q^{26} + 96 q^{27} - 88 q^{28} + 3 q^{29} - 29 q^{30} - 20 q^{31} - 143 q^{32} - 4 q^{33} - 22 q^{34} - 129 q^{35} - 43 q^{36} - 92 q^{37} - 83 q^{38} - 66 q^{39} - 15 q^{40} - 27 q^{41} - 73 q^{42} - 8 q^{43} - 92 q^{44} - 196 q^{45} - 80 q^{46} + 19 q^{47} - 130 q^{48} + 241 q^{49} + 7 q^{50} - 58 q^{51} - 63 q^{52} + 144 q^{53} - 85 q^{54} - 100 q^{55} - 71 q^{56} - 27 q^{57} - 395 q^{58} - 25 q^{59} + 36 q^{60} - 184 q^{61} - 107 q^{62} + 18 q^{63} + 450 q^{64} - 50 q^{65} - 79 q^{66} + 7 q^{67} - 138 q^{68} - 23 q^{69} - 47 q^{70} - 52 q^{71} - 753 q^{72} - 92 q^{73} + 32 q^{74} + 5 q^{75} + 3 q^{76} - 68 q^{77} - 136 q^{78} - 23 q^{79} - 56 q^{80} - 49 q^{81} - 92 q^{82} - 33 q^{83} - 292 q^{84} - 22 q^{85} + 27 q^{86} - 164 q^{87} + 18 q^{88} - 104 q^{89} + 351 q^{90} - 96 q^{91} + 1246 q^{92} - 106 q^{93} - 35 q^{94} + 387 q^{96} - 23 q^{97} - 775 q^{98} + 136 q^{99} + O(q^{100}) \)

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.