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Properties

Label 1859.2.b
Level $1859$
Weight $2$
Character orbit 1859.b
Rep. character $\chi_{1859}(1013,\cdot)$
Character field $\Q$
Dimension $128$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Sturm bound: \(364\)

Dimensions

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

Total New Old
Modular forms 196 128 68
Cusp forms 168 128 40
Eisenstein series 28 0 28

Trace form

\( 128 q + 4 q^{3} - 126 q^{4} + 128 q^{9} + O(q^{10}) \) \( 128 q + 4 q^{3} - 126 q^{4} + 128 q^{9} - 8 q^{10} + 130 q^{16} + 12 q^{17} + 2 q^{22} + 8 q^{23} - 120 q^{25} + 16 q^{27} - 12 q^{29} + 8 q^{30} - 32 q^{35} - 114 q^{36} - 8 q^{38} - 16 q^{40} - 20 q^{42} - 8 q^{43} + 48 q^{48} - 172 q^{49} + 12 q^{51} + 16 q^{53} + 8 q^{55} - 12 q^{56} + 12 q^{61} + 96 q^{62} - 118 q^{64} - 12 q^{66} - 80 q^{68} - 52 q^{69} - 32 q^{74} + 20 q^{75} - 8 q^{77} + 36 q^{79} + 176 q^{81} + 64 q^{82} - 20 q^{87} - 30 q^{88} - 56 q^{90} - 32 q^{92} + 56 q^{94} + 24 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1859, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)