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Properties

Label 1638.2.s
Level $1638$
Weight $2$
Character orbit 1638.s
Rep. character $\chi_{1638}(445,\cdot)$
Character field $\Q(\zeta_{3})$
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.s (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 819 \)
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 688 224 464
Cusp forms 656 224 432
Eisenstein series 32 0 32

Trace form

\( 224 q + 224 q^{4} + 8 q^{7} - 8 q^{9} + O(q^{10}) \) \( 224 q + 224 q^{4} + 8 q^{7} - 8 q^{9} + 8 q^{11} + 2 q^{13} - 16 q^{15} + 224 q^{16} - 16 q^{17} - 12 q^{18} - 8 q^{19} - 8 q^{21} - 4 q^{23} + 224 q^{25} - 4 q^{26} + 6 q^{27} + 8 q^{28} + 8 q^{29} - 8 q^{30} - 2 q^{31} + 16 q^{33} + 26 q^{35} - 8 q^{36} - 2 q^{37} + 48 q^{38} + 28 q^{39} - 8 q^{42} + 4 q^{43} + 8 q^{44} - 40 q^{45} + 6 q^{47} + 8 q^{49} + 8 q^{50} + 26 q^{51} + 2 q^{52} - 16 q^{53} - 6 q^{54} + 4 q^{57} - 16 q^{60} - 14 q^{61} - 38 q^{62} + 20 q^{63} + 224 q^{64} - 18 q^{65} - 14 q^{67} - 16 q^{68} - 18 q^{69} + 4 q^{71} - 12 q^{72} + 28 q^{73} + 6 q^{74} - 32 q^{75} - 8 q^{76} - 36 q^{77} - 4 q^{78} - 14 q^{79} + 4 q^{81} - 28 q^{83} - 8 q^{84} - 12 q^{85} + 16 q^{86} - 64 q^{87} + 10 q^{89} + 6 q^{90} + 26 q^{91} - 4 q^{92} - 52 q^{93} - 80 q^{95} + 4 q^{97} - 4 q^{99} + O(q^{100}) \)

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

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