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Properties

Label 1859.4.o
Level $1859$
Weight $4$
Character orbit 1859.o
Rep. character $\chi_{1859}(934,\cdot)$
Character field $\Q(\zeta_{12})$
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.o (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{12})\)
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

\( 1808 q + 4 q^{3} + 12 q^{4} + 8 q^{5} - 7772 q^{9} + O(q^{10}) \) \( 1808 q + 4 q^{3} + 12 q^{4} + 8 q^{5} - 7772 q^{9} + 80 q^{11} - 192 q^{14} + 76 q^{15} + 13796 q^{16} - 68 q^{20} - 188 q^{22} + 240 q^{23} - 920 q^{27} + 280 q^{31} + 266 q^{33} - 2212 q^{34} + 2760 q^{36} - 328 q^{37} - 1504 q^{42} - 104 q^{44} - 896 q^{45} - 4 q^{47} - 1148 q^{48} + 12 q^{49} + 8784 q^{53} - 586 q^{55} + 1356 q^{56} - 1096 q^{58} + 1392 q^{59} - 4 q^{60} + 6360 q^{66} - 304 q^{67} + 12 q^{69} + 1932 q^{70} + 5076 q^{71} - 8832 q^{75} - 4588 q^{80} - 58280 q^{81} + 7716 q^{82} - 5608 q^{86} - 10152 q^{88} - 7268 q^{89} - 13536 q^{92} - 2740 q^{93} - 2728 q^{97} + 6996 q^{99} + O(q^{100}) \)

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

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