Properties

Label 1840.2.x
Level $1840$
Weight $2$
Character orbit 1840.x
Rep. character $\chi_{1840}(461,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $352$
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.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
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 584 352 232
Cusp forms 568 352 216
Eisenstein series 16 0 16

Trace form

\( 352q + 12q^{6} + O(q^{10}) \) \( 352q + 12q^{6} + 12q^{12} - 16q^{14} + 40q^{18} - 16q^{20} + 48q^{22} - 8q^{24} + 32q^{26} - 24q^{27} + 48q^{28} - 40q^{34} - 12q^{36} - 40q^{42} - 72q^{44} + 80q^{47} - 352q^{49} + 80q^{51} - 48q^{52} - 32q^{54} + 56q^{56} + 20q^{58} - 8q^{59} + 56q^{60} + 76q^{62} - 12q^{64} - 80q^{66} + 16q^{70} - 36q^{72} + 40q^{74} - 60q^{78} - 32q^{80} - 352q^{81} + 116q^{82} - 80q^{83} + 32q^{84} + 16q^{86} - 40q^{88} - 72q^{90} - 64q^{91} + 48q^{93} - 48q^{94} - 64q^{95} + 120q^{96} - 56q^{98} - 64q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(368, [\chi])\)\(^{\oplus 2}\)