↑

Properties

Label 1840.2.r
Level $1840$
Weight $2$
Character orbit 1840.r
Rep. character $\chi_{1840}(413,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $568$
Sturm bound $576$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1840 \)
Character field: \(\Q(i)\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1840, [\chi])\).

Total New Old
Modular forms 584 584 0
Cusp forms 568 568 0
Eisenstein series 16 16 0

Trace form

\( 568 q - 4 q^{2} - 8 q^{4} - 8 q^{6} - 4 q^{8} - 552 q^{9} + O(q^{10}) \) \( 568 q - 4 q^{2} - 8 q^{4} - 8 q^{6} - 4 q^{8} - 552 q^{9} + 8 q^{12} - 16 q^{16} + 24 q^{24} - 8 q^{26} - 16 q^{31} - 24 q^{32} - 24 q^{35} - 8 q^{36} + 48 q^{39} - 20 q^{46} - 8 q^{47} - 76 q^{48} - 24 q^{50} + 8 q^{52} + 40 q^{54} + 20 q^{58} + 44 q^{62} - 32 q^{64} - 4 q^{69} - 16 q^{70} - 24 q^{72} + 8 q^{75} - 64 q^{77} - 28 q^{78} + 488 q^{81} + 4 q^{82} - 24 q^{85} + 24 q^{87} - 76 q^{92} - 8 q^{94} - 8 q^{95} - 8 q^{96} + 60 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1840, [\chi])\) into newform subspaces

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