↑

Properties

Label 1638.2.dn
Level $1638$
Weight $2$
Character orbit 1638.dn
Rep. character $\chi_{1638}(43,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $168$
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.dn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 688 168 520
Cusp forms 656 168 488
Eisenstein series 32 0 32

Trace form

\( 168 q + 84 q^{4} + 4 q^{9} + O(q^{10}) \) \( 168 q + 84 q^{4} + 4 q^{9} - 8 q^{14} - 84 q^{16} - 12 q^{18} + 12 q^{21} + 8 q^{23} + 84 q^{25} + 24 q^{27} - 44 q^{29} - 28 q^{30} - 8 q^{35} + 8 q^{36} + 12 q^{38} + 20 q^{39} + 60 q^{45} + 60 q^{47} - 168 q^{49} + 64 q^{51} + 48 q^{53} - 36 q^{54} - 16 q^{56} + 48 q^{57} - 96 q^{59} - 12 q^{60} - 12 q^{62} + 12 q^{63} - 168 q^{64} + 24 q^{65} + 16 q^{66} + 48 q^{69} - 12 q^{71} - 12 q^{72} + 112 q^{74} - 40 q^{75} + 16 q^{77} - 56 q^{78} + 12 q^{79} - 24 q^{81} + 24 q^{82} - 36 q^{83} + 12 q^{84} - 108 q^{85} + 24 q^{86} - 80 q^{87} + 36 q^{89} - 8 q^{90} + 12 q^{91} + 4 q^{92} + 96 q^{93} - 24 q^{95} - 48 q^{99} + O(q^{100}) \)

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

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