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Properties

Label 1710.2.by
Level $1710$
Weight $2$
Character orbit 1710.by
Rep. character $\chi_{1710}(493,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $480$
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.by (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 855 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 1472 480 992
Cusp forms 1408 480 928
Eisenstein series 64 0 64

Trace form

\( 480 q + O(q^{10}) \) \( 480 q + 240 q^{16} + 48 q^{17} + 16 q^{23} - 96 q^{35} - 12 q^{38} - 64 q^{42} + 136 q^{45} + 40 q^{47} + 4 q^{57} + 8 q^{63} - 16 q^{66} - 24 q^{68} + 96 q^{77} - 96 q^{81} + 64 q^{87} - 16 q^{92} + 56 q^{93} + 84 q^{95} + O(q^{100}) \)

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

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