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Properties

Label 1638.2.gg
Level $1638$
Weight $2$
Character orbit 1638.gg
Rep. character $\chi_{1638}(137,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $448$
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.gg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 819 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 1376 448 928
Cusp forms 1312 448 864
Eisenstein series 64 0 64

Trace form

\( 448 q - 8 q^{7} + O(q^{10}) \) \( 448 q - 8 q^{7} + 224 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} - 12 q^{27} - 4 q^{28} + 4 q^{31} + 36 q^{33} + 96 q^{35} + 4 q^{37} + 16 q^{39} + 24 q^{44} + 80 q^{45} - 36 q^{47} - 24 q^{50} + 4 q^{52} + 24 q^{53} - 12 q^{54} - 8 q^{57} - 24 q^{60} - 136 q^{63} + 84 q^{65} + 16 q^{66} - 28 q^{67} - 84 q^{69} - 24 q^{71} + 16 q^{72} + 56 q^{73} + 8 q^{76} + 24 q^{77} - 8 q^{78} + 48 q^{79} + 24 q^{81} - 8 q^{84} - 24 q^{85} - 48 q^{86} - 144 q^{87} - 60 q^{89} - 8 q^{91} - 24 q^{92} - 12 q^{93} + 4 q^{97} + 16 q^{99} + O(q^{100}) \)

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

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