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Properties

Label 1710.2.cf
Level $1710$
Weight $2$
Character orbit 1710.cf
Rep. character $\chi_{1710}(83,\cdot)$
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.cf (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

\( 480 q + O(q^{10}) \) \( 480 q + 12 q^{15} - 480 q^{16} + 36 q^{17} - 16 q^{18} - 12 q^{27} + 12 q^{33} - 96 q^{41} - 32 q^{42} - 32 q^{45} - 120 q^{47} + 96 q^{50} - 8 q^{51} + 16 q^{57} - 8 q^{60} + 28 q^{63} + 24 q^{65} - 64 q^{66} + 36 q^{68} + 16 q^{72} + 12 q^{75} + 48 q^{77} + 16 q^{78} + 48 q^{81} - 136 q^{87} + 8 q^{90} + 16 q^{93} - 60 q^{95} + 72 q^{98} + O(q^{100}) \)

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

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