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Properties

Label 1710.2.j
Level $1710$
Weight $2$
Character orbit 1710.j
Rep. character $\chi_{1710}(571,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $144$
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 736 144 592
Cusp forms 704 144 560
Eisenstein series 32 0 32

Trace form

\( 144 q - 72 q^{4} - 4 q^{5} + 8 q^{6} + 12 q^{9} + O(q^{10}) \) \( 144 q - 72 q^{4} - 4 q^{5} + 8 q^{6} + 12 q^{9} + 8 q^{11} + 4 q^{14} - 8 q^{15} - 72 q^{16} + 32 q^{17} - 16 q^{18} - 4 q^{20} - 8 q^{21} + 24 q^{23} - 4 q^{24} - 72 q^{25} - 32 q^{26} - 24 q^{27} - 12 q^{29} - 4 q^{30} + 32 q^{33} + 16 q^{35} - 12 q^{38} - 4 q^{39} - 44 q^{41} - 28 q^{42} - 16 q^{44} + 8 q^{45} - 24 q^{46} + 12 q^{47} - 60 q^{49} + 32 q^{51} - 32 q^{53} + 20 q^{54} + 4 q^{56} - 8 q^{60} + 12 q^{61} + 64 q^{62} - 32 q^{63} + 144 q^{64} + 8 q^{65} + 96 q^{66} - 16 q^{68} + 36 q^{69} + 12 q^{70} - 80 q^{71} - 16 q^{72} + 12 q^{74} + 8 q^{77} + 32 q^{78} + 24 q^{79} + 8 q^{80} - 4 q^{81} - 8 q^{83} - 20 q^{84} + 24 q^{85} + 24 q^{86} - 124 q^{87} - 88 q^{89} - 48 q^{91} + 24 q^{92} - 8 q^{93} + 12 q^{94} - 4 q^{96} + 16 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1710, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)