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Properties

Label 1710.2.da
Level $1710$
Weight $2$
Character orbit 1710.da
Rep. character $\chi_{1710}(89,\cdot)$
Character field $\Q(\zeta_{18})$
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.da (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 285 \)
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 2256 240 2016
Cusp forms 2064 240 1824
Eisenstein series 192 0 192

Trace form

\( 240 q + O(q^{10}) \) \( 240 q - 96 q^{19} - 24 q^{25} + 144 q^{46} + 72 q^{49} - 120 q^{55} + 144 q^{61} + 120 q^{64} - 96 q^{79} + 96 q^{85} - 24 q^{91} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1710, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)