Properties

Label 1859.4.n
Level $1859$
Weight $4$
Character orbit 1859.n
Rep. character $\chi_{1859}(168,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1808$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1859.n (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 2240 1888 352
Cusp forms 2128 1808 320
Eisenstein series 112 80 32

Trace form

\( 1808 q + 6 q^{3} + 1774 q^{4} - 3786 q^{9} + O(q^{10}) \) \( 1808 q + 6 q^{3} + 1774 q^{4} - 3786 q^{9} - 256 q^{10} - 108 q^{12} + 162 q^{14} - 6554 q^{16} + 122 q^{17} + 890 q^{22} - 184 q^{23} + 10594 q^{25} + 174 q^{27} + 22 q^{29} + 620 q^{30} - 1762 q^{35} + 14116 q^{36} + 376 q^{38} + 1082 q^{40} - 1274 q^{42} - 4720 q^{43} + 2478 q^{48} + 19674 q^{49} + 154 q^{51} + 3418 q^{53} - 438 q^{55} + 4764 q^{56} - 414 q^{61} - 2506 q^{62} + 19414 q^{64} - 4142 q^{66} + 4576 q^{68} - 3288 q^{69} - 4532 q^{74} + 974 q^{75} - 594 q^{77} + 1358 q^{79} - 34770 q^{81} - 8254 q^{82} + 9812 q^{87} + 8626 q^{88} + 14044 q^{90} - 10760 q^{92} - 1058 q^{94} - 2146 q^{95} + O(q^{100}) \)

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

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