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Properties

Label 1859.2.n
Level $1859$
Weight $2$
Character orbit 1859.n
Rep. character $\chi_{1859}(168,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $576$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.n (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(364\)

Dimensions

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

Total New Old
Modular forms 784 656 128
Cusp forms 672 576 96
Eisenstein series 112 80 32

Trace form

\( 576 q + 6 q^{3} + 140 q^{4} - 130 q^{9} + O(q^{10}) \) \( 576 q + 6 q^{3} + 140 q^{4} - 130 q^{9} + 56 q^{10} + 28 q^{12} - 50 q^{14} - 68 q^{16} - 18 q^{17} - 58 q^{22} + 36 q^{23} + 122 q^{25} - 54 q^{27} + 4 q^{29} - 96 q^{30} + 76 q^{35} + 50 q^{36} + 52 q^{38} + 6 q^{40} - 62 q^{42} + 48 q^{43} + 118 q^{48} + 78 q^{49} - 102 q^{51} + 12 q^{53} - 50 q^{55} - 124 q^{56} + 18 q^{61} - 78 q^{62} - 12 q^{64} + 122 q^{66} + 72 q^{68} + 16 q^{69} - 36 q^{74} - 126 q^{75} - 26 q^{77} - 42 q^{79} - 58 q^{81} - 14 q^{82} - 32 q^{87} - 150 q^{88} - 184 q^{90} - 52 q^{92} + 30 q^{94} + 122 q^{95} + O(q^{100}) \)

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

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