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Properties

Label 1710.2.bh
Level $1710$
Weight $2$
Character orbit 1710.bh
Rep. character $\chi_{1710}(619,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $240$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 855 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1710, [\chi])\).

Total New Old
Modular forms 736 240 496
Cusp forms 704 240 464
Eisenstein series 32 0 32

Trace form

\( 240 q + 120 q^{4} + O(q^{10}) \) \( 240 q + 120 q^{4} + 32 q^{14} - 16 q^{15} - 120 q^{16} + 24 q^{21} + 48 q^{29} - 10 q^{30} + 12 q^{35} + 24 q^{39} - 96 q^{41} - 48 q^{45} + 120 q^{49} + 20 q^{50} + 36 q^{54} + 16 q^{56} + 56 q^{59} - 14 q^{60} - 240 q^{64} - 38 q^{65} - 20 q^{66} + 8 q^{69} + 12 q^{71} - 16 q^{74} + 20 q^{75} - 24 q^{84} + 64 q^{86} - 48 q^{89} - 30 q^{90} + 30 q^{95} - 56 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1710, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1710, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1710, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(855, [\chi])\)\(^{\oplus 2}\)