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Properties

Label 1859.2.g
Level $1859$
Weight $2$
Character orbit 1859.g
Rep. character $\chi_{1859}(1253,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $288$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(i)\)
Sturm bound: \(364\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1859, [\chi])\).

Total New Old
Modular forms 392 328 64
Cusp forms 336 288 48
Eisenstein series 56 40 16

Trace form

\( 288 q + 8 q^{3} + 4 q^{5} + 256 q^{9} + O(q^{10}) \) \( 288 q + 8 q^{3} + 4 q^{5} + 256 q^{9} + 8 q^{11} - 8 q^{14} - 252 q^{16} - 16 q^{20} - 8 q^{22} - 40 q^{27} + 28 q^{31} + 12 q^{33} + 24 q^{34} - 8 q^{37} - 56 q^{42} - 4 q^{44} + 80 q^{45} - 32 q^{47} - 184 q^{48} - 96 q^{53} + 72 q^{55} - 56 q^{58} - 16 q^{59} - 28 q^{60} - 76 q^{66} + 20 q^{70} - 84 q^{71} + 88 q^{80} + 112 q^{81} + 68 q^{86} + 8 q^{89} - 80 q^{92} + 60 q^{93} - 20 q^{97} - 20 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1859, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1859, [\chi])\) into lower level spaces

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