Properties

Label 1840.2.u
Level $1840$
Weight $2$
Character orbit 1840.u
Rep. character $\chi_{1840}(91,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $384$
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.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 368 \)
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 584 384 200
Cusp forms 568 384 184
Eisenstein series 16 0 16

Trace form

\( 384q - 8q^{4} + 12q^{6} + O(q^{10}) \) \( 384q - 8q^{4} + 12q^{6} + 12q^{12} + 32q^{16} - 40q^{18} - 16q^{23} - 8q^{24} - 24q^{27} + 32q^{29} - 20q^{36} + 48q^{39} + 4q^{46} - 80q^{48} - 384q^{49} + 8q^{50} + 64q^{52} - 32q^{54} + 76q^{58} - 24q^{59} - 60q^{62} - 44q^{64} + 16q^{69} + 188q^{72} - 32q^{77} - 92q^{78} - 384q^{81} + 36q^{82} + 32q^{85} + 12q^{92} + 48q^{93} + 72q^{94} - 136q^{96} + 208q^{98} + O(q^{100}) \)

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

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