Properties

Label 1710.2.cp
Level $1710$
Weight $2$
Character orbit 1710.cp
Rep. character $\chi_{1710}(41,\cdot)$
Character field $\Q(\zeta_{18})$
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.cp (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
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 480 1728
Cusp forms 2112 480 1632
Eisenstein series 96 0 96

Trace form

\( 480 q + 12 q^{3} + 12 q^{6} - 12 q^{9} + O(q^{10}) \) \( 480 q + 12 q^{3} + 12 q^{6} - 12 q^{9} - 12 q^{13} - 12 q^{19} + 18 q^{22} - 6 q^{24} + 18 q^{27} - 12 q^{28} - 60 q^{33} - 12 q^{36} - 12 q^{39} + 12 q^{43} + 6 q^{48} - 240 q^{49} + 24 q^{51} - 24 q^{52} + 36 q^{54} + 24 q^{57} + 180 q^{59} - 84 q^{61} + 48 q^{63} - 240 q^{64} + 30 q^{66} - 204 q^{67} + 18 q^{68} + 6 q^{72} + 48 q^{73} - 72 q^{78} + 24 q^{79} - 156 q^{81} + 18 q^{82} + 144 q^{83} + 12 q^{87} + 108 q^{89} - 24 q^{90} + 24 q^{91} - 36 q^{97} - 66 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1710, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(855, [\chi])\)\(^{\oplus 2}\)