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Properties

Label 1638.2.eg
Level $1638$
Weight $2$
Character orbit 1638.eg
Rep. character $\chi_{1638}(185,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $224$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.eg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 819 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1638, [\chi])\).

Total New Old
Modular forms 688 224 464
Cusp forms 656 224 432
Eisenstein series 32 0 32

Trace form

\( 224 q - 224 q^{4} - 8 q^{7} - 8 q^{9} + O(q^{10}) \) \( 224 q - 224 q^{4} - 8 q^{7} - 8 q^{9} - 24 q^{11} - 6 q^{13} + 224 q^{16} - 12 q^{18} - 8 q^{21} - 12 q^{23} + 224 q^{25} - 12 q^{26} - 18 q^{27} + 8 q^{28} + 8 q^{30} - 6 q^{31} - 72 q^{33} - 18 q^{35} + 8 q^{36} + 2 q^{37} + 20 q^{42} - 4 q^{43} + 24 q^{44} + 18 q^{47} + 8 q^{49} - 14 q^{51} + 6 q^{52} - 12 q^{53} + 18 q^{54} - 4 q^{57} - 42 q^{61} + 18 q^{62} + 8 q^{63} - 224 q^{64} - 54 q^{65} - 24 q^{66} - 14 q^{67} + 54 q^{69} + 12 q^{71} + 12 q^{72} - 18 q^{74} - 108 q^{75} + 12 q^{77} + 12 q^{78} + 10 q^{79} - 4 q^{81} + 8 q^{84} + 12 q^{85} + 24 q^{87} - 30 q^{89} + 18 q^{90} + 30 q^{91} + 12 q^{92} - 68 q^{93} - 48 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1638, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1638, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1638, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(819, [\chi])\)\(^{\oplus 2}\)