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Properties

Label 2738.2.l
Level $2738$
Weight $2$
Character orbit 2738.l
Rep. character $\chi_{2738}(47,\cdot)$
Character field $\Q(\zeta_{111})$
Dimension $8568$
Sturm bound $703$

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Defining parameters

Level: \( N \) \(=\) \( 2738 = 2 \cdot 37^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2738.l (of order \(111\) and degree \(72\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1369 \)
Character field: \(\Q(\zeta_{111})\)
Sturm bound: \(703\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2738, [\chi])\).

Total New Old
Modular forms 25416 8568 16848
Cusp forms 25128 8568 16560
Eisenstein series 288 0 288

Trace form

\( 8568 q + q^{2} + 119 q^{4} + 3 q^{5} - 4 q^{7} - 2 q^{8} + 123 q^{9} + O(q^{10}) \) \( 8568 q + q^{2} + 119 q^{4} + 3 q^{5} - 4 q^{7} - 2 q^{8} + 123 q^{9} + 2 q^{10} + 2 q^{13} - 8 q^{14} - 4 q^{15} + 119 q^{16} + 3 q^{17} - 180 q^{18} + 12 q^{19} + 3 q^{20} - 8 q^{21} + 8 q^{22} - 16 q^{23} + 134 q^{25} - 20 q^{26} - 198 q^{27} - 4 q^{28} + 18 q^{29} + 12 q^{30} - 32 q^{31} + q^{32} + 4 q^{33} + 361 q^{34} - 16 q^{35} - 246 q^{36} + q^{37} - 4 q^{38} - 16 q^{39} - q^{40} + 145 q^{41} - 24 q^{42} + 8 q^{43} - 70 q^{45} + 6 q^{46} + 40 q^{47} + 111 q^{49} + 20 q^{50} + 64 q^{51} + 2 q^{52} + 8 q^{53} - 12 q^{54} + 12 q^{55} + 4 q^{56} - 20 q^{57} + 3 q^{58} + 12 q^{59} + 8 q^{60} + 3 q^{61} - 10 q^{62} - 16 q^{63} - 238 q^{64} - 68 q^{65} + 56 q^{66} + 416 q^{67} - 6 q^{68} - 250 q^{69} + 8 q^{70} - 32 q^{71} + 5 q^{72} + 24 q^{73} - 18 q^{74} - 36 q^{75} + 12 q^{76} + 28 q^{77} + 6 q^{78} + 16 q^{79} - 43 q^{80} + 251 q^{81} + 26 q^{82} + 446 q^{83} - 206 q^{84} + 22 q^{85} + 18 q^{86} - 156 q^{87} - 16 q^{88} + 147 q^{89} + 21 q^{90} + 584 q^{91} - 66 q^{92} + 36 q^{93} - 12 q^{94} - 40 q^{95} - 6 q^{97} - 303 q^{98} + 38 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2738, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2738, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2738, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1369, [\chi])\)\(^{\oplus 2}\)