Properties

Label 2738.2.k
Level $2738$
Weight $2$
Character orbit 2738.k
Rep. character $\chi_{2738}(73,\cdot)$
Character field $\Q(\zeta_{74})$
Dimension $4248$
Sturm bound $703$

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Defining parameters

Level: \( N \) \(=\) \( 2738 = 2 \cdot 37^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2738.k (of order \(74\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1369 \)
Character field: \(\Q(\zeta_{74})\)
Sturm bound: \(703\)

Dimensions

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

Total New Old
Modular forms 12744 4248 8496
Cusp forms 12600 4248 8352
Eisenstein series 144 0 144

Trace form

\( 4248 q + 2 q^{3} + 118 q^{4} + 8 q^{7} - 124 q^{9} + O(q^{10}) \) \( 4248 q + 2 q^{3} + 118 q^{4} + 8 q^{7} - 124 q^{9} + 6 q^{10} - 6 q^{11} - 2 q^{12} - 118 q^{16} - 4 q^{21} + 124 q^{25} + 6 q^{26} - 202 q^{27} - 8 q^{28} - 24 q^{30} + 24 q^{33} - 12 q^{34} + 124 q^{36} - 16 q^{37} + 14 q^{38} - 6 q^{40} - 32 q^{41} + 6 q^{44} + 8 q^{46} + 12 q^{47} + 2 q^{48} - 102 q^{49} - 10 q^{53} - 6 q^{58} + 4 q^{62} + 20 q^{63} + 118 q^{64} + 54 q^{65} + 216 q^{67} - 222 q^{69} - 12 q^{70} + 8 q^{71} - 12 q^{73} - 58 q^{75} + 4 q^{77} + 8 q^{78} - 168 q^{81} - 236 q^{83} - 218 q^{84} + 16 q^{85} + 26 q^{86} - 148 q^{87} - 74 q^{89} + 46 q^{90} - 296 q^{91} + 74 q^{92} + 52 q^{95} - 296 q^{98} - 46 q^{99} + O(q^{100}) \)

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

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