↑

Properties

Label 1638.2.gj
Level $1638$
Weight $2$
Character orbit 1638.gj
Rep. character $\chi_{1638}(241,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $448$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.gj (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 819 \)
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 448 928
Cusp forms 1312 448 864
Eisenstein series 64 0 64

Trace form

\( 448 q + 8 q^{7} + O(q^{10}) \) \( 448 q + 8 q^{7} + 16 q^{11} - 16 q^{15} + 224 q^{16} + 16 q^{18} + 8 q^{21} - 36 q^{27} - 4 q^{28} - 16 q^{29} + 12 q^{31} - 60 q^{33} - 32 q^{35} - 4 q^{37} + 24 q^{42} - 8 q^{44} - 36 q^{47} - 8 q^{50} + 12 q^{52} + 8 q^{53} + 36 q^{54} + 8 q^{57} - 8 q^{60} + 24 q^{63} - 28 q^{65} - 28 q^{67} + 84 q^{69} - 24 q^{71} - 16 q^{72} + 24 q^{77} - 8 q^{78} - 48 q^{79} - 104 q^{81} + 8 q^{84} + 24 q^{85} + 16 q^{86} + 48 q^{87} + 60 q^{89} + 8 q^{91} + 8 q^{92} + 52 q^{93} + 48 q^{95} + 12 q^{97} - 16 q^{98} + O(q^{100}) \)

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

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