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Properties

Label 1710.2.cj
Level $1710$
Weight $2$
Character orbit 1710.cj
Rep. character $\chi_{1710}(217,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $200$
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.cj (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
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 1504 200 1304
Cusp forms 1376 200 1176
Eisenstein series 128 0 128

Trace form

\( 200 q + 4 q^{5} + 8 q^{7} + O(q^{10}) \) \( 200 q + 4 q^{5} + 8 q^{7} - 8 q^{11} + 100 q^{16} + 8 q^{17} + 24 q^{22} - 12 q^{23} - 12 q^{25} - 16 q^{26} - 4 q^{28} + 16 q^{35} - 20 q^{38} + 12 q^{41} - 4 q^{43} + 44 q^{47} - 36 q^{53} + 40 q^{55} + 16 q^{61} + 8 q^{62} + 72 q^{67} - 16 q^{68} + 24 q^{70} - 24 q^{73} - 24 q^{76} + 128 q^{77} - 4 q^{80} + 8 q^{82} + 64 q^{83} - 12 q^{85} + 24 q^{86} + 120 q^{91} + 12 q^{92} + 44 q^{95} + 84 q^{97} - 24 q^{98} + O(q^{100}) \)

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

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