Properties

Label 1638.2.i
Level $1638$
Weight $2$
Character orbit 1638.i
Rep. character $\chi_{1638}(625,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $192$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 688 192 496
Cusp forms 656 192 464
Eisenstein series 32 0 32

Trace form

\( 192 q + 192 q^{4} + 8 q^{5} + 8 q^{6} + 8 q^{9} + O(q^{10}) \) \( 192 q + 192 q^{4} + 8 q^{5} + 8 q^{6} + 8 q^{9} - 4 q^{14} - 12 q^{15} + 192 q^{16} + 12 q^{17} + 8 q^{20} + 32 q^{21} + 12 q^{23} + 8 q^{24} - 96 q^{25} + 12 q^{26} + 6 q^{27} + 4 q^{29} - 10 q^{30} + 24 q^{33} + 36 q^{35} + 8 q^{36} + 12 q^{41} + 22 q^{42} + 4 q^{45} + 12 q^{46} - 12 q^{49} + 16 q^{50} - 32 q^{51} - 16 q^{53} - 16 q^{54} + 24 q^{55} - 4 q^{56} - 44 q^{57} - 12 q^{58} - 88 q^{59} - 12 q^{60} - 24 q^{61} - 12 q^{62} + 8 q^{63} + 192 q^{64} + 32 q^{66} + 12 q^{68} - 64 q^{69} + 36 q^{70} - 88 q^{71} - 16 q^{75} - 76 q^{77} + 24 q^{79} + 8 q^{80} - 40 q^{81} + 24 q^{83} + 32 q^{84} - 8 q^{86} + 24 q^{87} + 52 q^{89} + 2 q^{90} + 12 q^{92} + 12 q^{93} + 48 q^{94} + 104 q^{95} + 8 q^{96} + 48 q^{98} + 132 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1638, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(819, [\chi])\)\(^{\oplus 2}\)