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Properties

Label 2738.2.c
Level $2738$
Weight $2$
Character orbit 2738.c
Rep. character $\chi_{2738}(581,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $218$
Sturm bound $703$

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Defining parameters

Level: \( N \) \(=\) \( 2738 = 2 \cdot 37^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2738.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(703\)

Dimensions

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

Total New Old
Modular forms 778 218 560
Cusp forms 626 218 408
Eisenstein series 152 0 152

Trace form

\( 218 q + q^{2} - 109 q^{4} + 3 q^{5} - 4 q^{7} - 2 q^{8} - 105 q^{9} + O(q^{10}) \) \( 218 q + q^{2} - 109 q^{4} + 3 q^{5} - 4 q^{7} - 2 q^{8} - 105 q^{9} + 2 q^{10} + 2 q^{13} - 8 q^{14} - 4 q^{15} - 109 q^{16} + 3 q^{17} + 5 q^{18} + 12 q^{19} + 3 q^{20} - 8 q^{21} + 8 q^{22} - 16 q^{23} - 94 q^{25} - 20 q^{26} + 24 q^{27} - 4 q^{28} + 18 q^{29} + 12 q^{30} - 32 q^{31} + q^{32} + 4 q^{33} - 9 q^{34} - 16 q^{35} + 210 q^{36} - 12 q^{38} - 16 q^{39} - q^{40} + q^{41} - 24 q^{42} + 8 q^{43} - 70 q^{45} + 10 q^{46} + 40 q^{47} - 117 q^{49} + 20 q^{50} + 64 q^{51} + 2 q^{52} + 12 q^{53} - 12 q^{54} + 12 q^{55} + 4 q^{56} - 20 q^{57} + 3 q^{58} + 12 q^{59} + 8 q^{60} + 3 q^{61} - 6 q^{62} - 16 q^{63} + 218 q^{64} + 22 q^{65} + 56 q^{66} - 12 q^{67} - 6 q^{68} - 28 q^{69} + 8 q^{70} - 16 q^{71} + 5 q^{72} + 16 q^{73} - 76 q^{75} + 12 q^{76} + 44 q^{77} + 26 q^{78} + 16 q^{79} - 6 q^{80} - 125 q^{81} + 26 q^{82} + 22 q^{83} + 16 q^{84} - 10 q^{85} + 22 q^{86} - 8 q^{87} - 16 q^{88} - q^{89} + 41 q^{90} - 8 q^{91} + 8 q^{92} + 36 q^{93} - 12 q^{94} - 24 q^{95} - 6 q^{97} - 7 q^{98} + 58 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2738, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1369, [\chi])\)\(^{\oplus 2}\)