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Properties

Label 2738.2.e
Level $2738$
Weight $2$
Character orbit 2738.e
Rep. character $\chi_{2738}(1951,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $220$
Sturm bound $703$

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Defining parameters

Level: \( N \) \(=\) \( 2738 = 2 \cdot 37^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2738.e (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(703\)

Dimensions

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

Total New Old
Modular forms 780 220 560
Cusp forms 628 220 408
Eisenstein series 152 0 152

Trace form

\( 220 q + 4 q^{3} + 110 q^{4} + 4 q^{7} - 110 q^{9} + O(q^{10}) \) \( 220 q + 4 q^{3} + 110 q^{4} + 4 q^{7} - 110 q^{9} - 4 q^{12} + 12 q^{13} - 110 q^{16} + 4 q^{21} + 122 q^{25} + 24 q^{26} - 32 q^{27} - 4 q^{28} + 12 q^{30} - 12 q^{33} - 12 q^{34} - 36 q^{35} - 220 q^{36} - 4 q^{38} + 24 q^{39} - 2 q^{41} - 36 q^{42} - 10 q^{46} - 24 q^{47} - 8 q^{48} - 102 q^{49} + 12 q^{52} + 2 q^{53} + 36 q^{55} + 36 q^{57} + 12 q^{58} - 36 q^{61} + 10 q^{62} - 8 q^{63} - 220 q^{64} + 4 q^{65} - 16 q^{67} + 20 q^{71} - 4 q^{73} - 36 q^{75} + 28 q^{77} - 34 q^{78} + 12 q^{79} - 110 q^{81} + 22 q^{83} + 8 q^{84} - 8 q^{85} - 22 q^{86} + 72 q^{87} - 36 q^{89} + 34 q^{90} + 24 q^{91} + 12 q^{93} - 36 q^{94} + 4 q^{95} - 34 q^{99} + O(q^{100}) \)

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

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