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Properties

Label 1638.2.fc
Level $1638$
Weight $2$
Character orbit 1638.fc
Rep. character $\chi_{1638}(515,\cdot)$
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.fc (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

\( 448 q + 4 q^{7} + O(q^{10}) \) \( 448 q + 4 q^{7} - 24 q^{11} - 24 q^{15} - 448 q^{16} - 8 q^{18} + 8 q^{19} + 8 q^{21} - 12 q^{27} - 4 q^{28} - 8 q^{31} - 24 q^{33} + 120 q^{35} + 4 q^{37} - 8 q^{39} - 36 q^{42} + 24 q^{44} + 80 q^{45} - 24 q^{50} + 4 q^{52} - 48 q^{53} - 12 q^{54} - 8 q^{57} - 24 q^{60} + 8 q^{63} - 32 q^{66} + 56 q^{67} - 8 q^{72} + 56 q^{73} + 8 q^{76} + 16 q^{78} - 96 q^{79} - 48 q^{81} - 8 q^{84} - 24 q^{85} + 48 q^{86} + 96 q^{87} + 60 q^{89} + 4 q^{91} + 48 q^{92} - 48 q^{93} + 4 q^{97} - 48 q^{98} - 8 q^{99} + O(q^{100}) \)

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

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