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Properties

Label 1710.2.cx
Level $1710$
Weight $2$
Character orbit 1710.cx
Rep. character $\chi_{1710}(199,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $300$
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.cx (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
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 300 1956
Cusp forms 2064 300 1764
Eisenstein series 192 0 192

Trace form

\( 300 q + O(q^{10}) \) \( 300 q + 12 q^{11} - 12 q^{14} + 48 q^{19} - 12 q^{20} + 48 q^{25} + 6 q^{26} - 24 q^{29} + 6 q^{35} - 6 q^{41} + 6 q^{44} + 48 q^{46} + 138 q^{49} - 24 q^{50} - 18 q^{55} + 48 q^{56} - 84 q^{59} + 120 q^{61} + 150 q^{64} - 30 q^{65} - 36 q^{70} + 144 q^{71} + 18 q^{74} - 6 q^{76} + 108 q^{79} + 24 q^{85} + 24 q^{86} + 60 q^{89} + 60 q^{91} + 108 q^{94} + 36 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1710, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(855, [\chi])\)\(^{\oplus 2}\)