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Properties

Label 1859.4.g
Level $1859$
Weight $4$
Character orbit 1859.g
Rep. character $\chi_{1859}(1253,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $904$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1859.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(i)\)
Sturm bound: \(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1859, [\chi])\).

Total New Old
Modular forms 1120 944 176
Cusp forms 1064 904 160
Eisenstein series 56 40 16

Trace form

\( 904 q + 8 q^{3} + 4 q^{5} + 7784 q^{9} + O(q^{10}) \) \( 904 q + 8 q^{3} + 4 q^{5} + 7784 q^{9} - 14 q^{11} - 408 q^{14} + 80 q^{15} - 13784 q^{16} + 200 q^{20} + 584 q^{22} + 800 q^{27} - 208 q^{31} - 860 q^{33} + 232 q^{34} + 340 q^{37} - 968 q^{42} + 644 q^{44} + 1148 q^{45} + 280 q^{47} - 3352 q^{48} - 1848 q^{53} - 1748 q^{55} + 1972 q^{58} + 84 q^{59} - 1484 q^{60} + 7164 q^{66} - 2468 q^{67} + 3540 q^{70} - 1704 q^{71} + 3544 q^{80} + 56744 q^{81} - 32 q^{86} - 424 q^{89} - 2544 q^{92} - 3944 q^{93} + 4936 q^{97} + 3750 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1859, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1859, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1859, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)