Properties

Label 1840.2.bg
Level $1840$
Weight $2$
Character orbit 1840.bg
Rep. character $\chi_{1840}(829,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $528$
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.bg (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
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 584 528 56
Cusp forms 568 528 40
Eisenstein series 16 0 16

Trace form

\( 528q + O(q^{10}) \) \( 528q + 12q^{10} - 16q^{14} + 28q^{20} + 32q^{24} - 32q^{26} + 52q^{30} - 48q^{31} + 24q^{35} - 80q^{36} - 40q^{44} + 528q^{49} - 12q^{50} + 56q^{54} - 32q^{59} - 116q^{60} - 24q^{64} + 16q^{65} + 200q^{66} - 108q^{70} + 88q^{74} - 88q^{75} + 120q^{76} - 28q^{80} - 528q^{81} + 96q^{84} + 64q^{86} + 124q^{90} - 32q^{91} + 56q^{94} - 48q^{95} - 40q^{96} - 64q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)