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Properties

Label 1638.4.fl
Level $1638$
Weight $4$
Character orbit 1638.fl
Rep. character $\chi_{1638}(743,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1008$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1638.fl (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1638, [\chi])\).

Total New Old
Modular forms 4064 1008 3056
Cusp forms 4000 1008 2992
Eisenstein series 64 0 64

Trace form

\( 1008 q + O(q^{10}) \) \( 1008 q - 48 q^{11} + 168 q^{15} + 8064 q^{16} - 32 q^{18} + 224 q^{21} + 1248 q^{27} + 816 q^{30} + 624 q^{33} + 144 q^{38} - 1520 q^{39} - 3072 q^{41} - 2584 q^{45} + 2256 q^{50} - 192 q^{54} - 656 q^{57} - 288 q^{60} + 1064 q^{63} + 5688 q^{65} + 1984 q^{66} + 1752 q^{71} - 128 q^{72} - 14040 q^{75} - 5312 q^{78} - 1872 q^{79} + 2160 q^{81} + 4584 q^{83} - 896 q^{84} - 8064 q^{85} + 9600 q^{89} + 1248 q^{92} + 1656 q^{93} - 3168 q^{97} - 8432 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1638, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1638, [\chi])\) into lower level spaces

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