Properties

Label 1840.2.bk
Level $1840$
Weight $2$
Character orbit 1840.bk
Rep. character $\chi_{1840}(323,\cdot)$
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.bk (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

\( 528 q + 12 q^{8} + 528 q^{9} + O(q^{10}) \) \( 528 q + 12 q^{8} + 528 q^{9} - 16 q^{12} + 28 q^{18} + 12 q^{20} - 16 q^{22} + 32 q^{26} - 12 q^{28} - 56 q^{30} - 40 q^{32} - 16 q^{34} - 24 q^{35} - 44 q^{38} - 28 q^{40} + 40 q^{42} + 32 q^{44} - 48 q^{47} + 28 q^{48} + 28 q^{50} - 16 q^{52} - 32 q^{54} - 76 q^{58} - 32 q^{59} + 40 q^{60} + 60 q^{62} - 16 q^{66} + 72 q^{68} + 104 q^{70} - 64 q^{71} + 80 q^{72} + 16 q^{73} + 56 q^{74} - 24 q^{75} + 124 q^{78} + 108 q^{80} + 528 q^{81} - 76 q^{82} - 120 q^{84} + 16 q^{86} - 112 q^{87} + 60 q^{88} - 44 q^{90} - 32 q^{91} + 48 q^{94} + 104 q^{96} + 160 q^{98} - 64 q^{99} + O(q^{100}) \)

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

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