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Properties

Label 1840.4.bg
Level $1840$
Weight $4$
Character orbit 1840.bg
Rep. character $\chi_{1840}(829,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $1584$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1840.bg (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1840, [\chi])\).

Total New Old
Modular forms 1736 1584 152
Cusp forms 1720 1584 136
Eisenstein series 16 0 16

Trace form

\( 1584 q + O(q^{10}) \) \( 1584 q - 12 q^{10} + 208 q^{14} - 308 q^{20} - 736 q^{24} + 544 q^{26} - 1444 q^{30} + 1488 q^{31} - 456 q^{35} + 880 q^{36} + 2296 q^{44} + 77616 q^{49} - 1428 q^{50} - 2968 q^{54} + 1376 q^{59} - 3044 q^{60} + 6888 q^{64} - 976 q^{65} - 4360 q^{66} + 5148 q^{70} - 4312 q^{74} + 1096 q^{75} - 6120 q^{76} - 3932 q^{80} - 128304 q^{81} - 11040 q^{84} + 7872 q^{86} - 3324 q^{90} - 1696 q^{91} + 7336 q^{94} - 7728 q^{95} + 9560 q^{96} + 5312 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1840, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1840, [\chi])\) into lower level spaces

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