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Properties

Label 1710.2.dc
Level $1710$
Weight $2$
Character orbit 1710.dc
Rep. character $\chi_{1710}(499,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $720$
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.dc (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 855 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 2208 720 1488
Cusp forms 2112 720 1392
Eisenstein series 96 0 96

Trace form

\( 720 q + O(q^{10}) \) \( 720 q + 48 q^{15} - 36 q^{35} - 24 q^{39} - 54 q^{45} + 360 q^{49} + 48 q^{50} - 36 q^{54} + 48 q^{56} + 120 q^{59} + 6 q^{60} + 360 q^{64} - 120 q^{65} - 12 q^{66} + 72 q^{71} - 240 q^{81} + 36 q^{84} - 54 q^{90} + 6 q^{95} - 12 q^{99} + O(q^{100}) \)

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

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