Properties

Label 1710.2.dh
Level $1710$
Weight $2$
Character orbit 1710.dh
Rep. character $\chi_{1710}(47,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1440$
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.dh (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 855 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 4416 1440 2976
Cusp forms 4224 1440 2784
Eisenstein series 192 0 192

Trace form

\( 1440 q + O(q^{10}) \) \( 1440 q + 72 q^{15} + 108 q^{17} + 24 q^{18} + 72 q^{23} - 36 q^{33} + 72 q^{45} + 24 q^{51} - 216 q^{57} + 24 q^{60} - 36 q^{63} - 24 q^{66} - 48 q^{78} - 96 q^{87} + 12 q^{90} + 60 q^{93} + 216 q^{98} + O(q^{100}) \)

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

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