Properties

Label 1638.2.gh
Level $1638$
Weight $2$
Character orbit 1638.gh
Rep. character $\chi_{1638}(239,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $336$
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.gh (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 1376 336 1040
Cusp forms 1312 336 976
Eisenstein series 64 0 64

Trace form

\( 336 q + O(q^{10}) \) \( 336 q - 24 q^{11} + 24 q^{15} + 168 q^{16} - 8 q^{18} + 8 q^{21} + 96 q^{27} + 48 q^{33} + 40 q^{39} + 96 q^{41} - 160 q^{45} + 120 q^{47} + 24 q^{50} + 24 q^{54} - 8 q^{57} + 8 q^{63} + 72 q^{65} - 32 q^{66} + 16 q^{72} + 96 q^{74} - 104 q^{78} - 48 q^{79} + 48 q^{83} + 16 q^{84} - 24 q^{85} + 48 q^{86} - 48 q^{92} - 72 q^{93} - 48 q^{97} - 80 q^{99} + O(q^{100}) \)

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

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