Properties

Label 1840.2.cw
Level $1840$
Weight $2$
Character orbit 1840.cw
Rep. character $\chi_{1840}(11,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $3840$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.cw (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 368 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 5840 3840 2000
Cusp forms 5680 3840 1840
Eisenstein series 160 0 160

Trace form

\( 3840q + 8q^{4} - 12q^{6} + O(q^{10}) \) \( 3840q + 8q^{4} - 12q^{6} - 12q^{12} - 32q^{16} + 40q^{18} + 16q^{23} + 8q^{24} + 24q^{27} - 32q^{29} + 44q^{34} + 20q^{36} - 220q^{38} - 48q^{39} - 356q^{46} + 80q^{48} + 384q^{49} + 36q^{50} - 64q^{52} - 144q^{54} + 144q^{58} + 24q^{59} + 60q^{62} + 44q^{64} - 16q^{69} - 188q^{72} - 144q^{77} + 92q^{78} + 384q^{81} - 36q^{82} - 32q^{85} - 12q^{92} + 480q^{93} - 72q^{94} + 136q^{96} - 208q^{98} + O(q^{100}) \)

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

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

Decomposition of \(S_{2}^{\mathrm{old}}(1840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(368, [\chi])\)\(^{\oplus 2}\)