Properties

Label 1638.2.cv
Level $1638$
Weight $2$
Character orbit 1638.cv
Rep. character $\chi_{1638}(277,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $224$
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.cv (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 819 \)
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 688 224 464
Cusp forms 656 224 432
Eisenstein series 32 0 32

Trace form

\( 224 q + 112 q^{4} - 4 q^{9} + O(q^{10}) \) \( 224 q + 112 q^{4} - 4 q^{9} - 2 q^{13} - 112 q^{16} + 32 q^{17} - 12 q^{18} - 12 q^{19} + 4 q^{23} + 112 q^{25} - 8 q^{26} + 6 q^{27} + 8 q^{29} - 14 q^{30} - 12 q^{33} - 4 q^{35} - 8 q^{36} - 24 q^{38} - 20 q^{39} - 4 q^{42} + 4 q^{43} + 60 q^{45} + 8 q^{49} + 12 q^{51} + 2 q^{52} + 24 q^{53} - 12 q^{57} - 12 q^{60} + 14 q^{61} - 26 q^{62} + 48 q^{63} - 224 q^{64} - 22 q^{65} + 16 q^{66} + 42 q^{67} + 16 q^{68} - 10 q^{69} + 36 q^{71} - 84 q^{73} - 6 q^{74} - 108 q^{75} - 20 q^{77} - 4 q^{78} + 20 q^{79} - 44 q^{81} - 84 q^{83} + 36 q^{85} + 24 q^{86} + 44 q^{87} - 6 q^{90} + 18 q^{91} - 4 q^{92} + 36 q^{93} - 24 q^{95} - 24 q^{98} - 12 q^{99} + O(q^{100}) \)

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

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