Properties

Label 1638.2.dk
Level $1638$
Weight $2$
Character orbit 1638.dk
Rep. character $\chi_{1638}(121,\cdot)$
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.dk (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

\( 224 q + 112 q^{4} + 8 q^{9} + O(q^{10}) \) \( 224 q + 112 q^{4} + 8 q^{9} - 2 q^{13} + 12 q^{15} - 112 q^{16} - 16 q^{17} + 12 q^{18} - 8 q^{23} + 112 q^{25} + 4 q^{26} + 6 q^{27} - 16 q^{29} + 16 q^{30} - 12 q^{33} + 26 q^{35} + 4 q^{36} - 6 q^{37} - 24 q^{38} - 2 q^{39} - 4 q^{42} - 2 q^{43} + 60 q^{45} - 4 q^{49} + 12 q^{50} + 12 q^{51} - 4 q^{52} + 24 q^{53} - 18 q^{54} + 12 q^{57} + 12 q^{60} + 14 q^{61} - 26 q^{62} + 18 q^{63} - 224 q^{64} - 22 q^{65} + 16 q^{66} + 42 q^{67} - 32 q^{68} + 32 q^{69} + 36 q^{71} + 12 q^{72} + 84 q^{73} + 12 q^{74} + 36 q^{75} - 12 q^{76} - 20 q^{77} - 4 q^{78} + 20 q^{79} + 28 q^{81} + 84 q^{83} - 24 q^{86} - 28 q^{87} + 30 q^{89} - 6 q^{90} - 30 q^{91} - 4 q^{92} - 24 q^{95} + 6 q^{97} + 12 q^{99} + O(q^{100}) \)

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

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