Properties

Label 1638.2.k
Level $1638$
Weight $2$
Character orbit 1638.k
Rep. character $\chi_{1638}(211,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $168$
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.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 688 168 520
Cusp forms 656 168 488
Eisenstein series 32 0 32

Trace form

\( 168 q - 84 q^{4} - 4 q^{9} + O(q^{10}) \) \( 168 q - 84 q^{4} - 4 q^{9} - 8 q^{11} + 8 q^{14} + 16 q^{15} - 84 q^{16} - 4 q^{18} - 4 q^{21} - 8 q^{23} - 84 q^{25} + 24 q^{27} + 28 q^{29} + 20 q^{30} - 24 q^{33} + 8 q^{35} + 8 q^{36} + 12 q^{38} + 28 q^{39} - 32 q^{41} + 16 q^{44} - 60 q^{45} + 68 q^{47} + 168 q^{49} - 8 q^{50} + 16 q^{51} - 48 q^{53} - 60 q^{54} - 16 q^{56} + 48 q^{57} - 32 q^{59} + 4 q^{60} + 12 q^{62} - 4 q^{63} + 168 q^{64} + 32 q^{65} + 16 q^{66} + 48 q^{69} + 4 q^{71} - 4 q^{72} - 48 q^{74} - 40 q^{75} + 16 q^{77} - 40 q^{78} + 12 q^{79} + 32 q^{81} - 24 q^{82} - 28 q^{83} - 4 q^{84} - 12 q^{85} + 8 q^{86} + 80 q^{87} - 28 q^{89} + 8 q^{90} - 12 q^{91} + 4 q^{92} - 16 q^{93} + 8 q^{95} - 96 q^{97} - 24 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1638, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(819, [\chi])\)\(^{\oplus 2}\)