Properties

Label 1470.2.t
Level $1470$
Weight $2$
Character orbit 1470.t
Rep. character $\chi_{1470}(509,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1470, [\chi])\).

Total New Old
Modular forms 736 160 576
Cusp forms 608 160 448
Eisenstein series 128 0 128

Trace form

\( 160q - 80q^{4} - 10q^{9} + O(q^{10}) \) \( 160q - 80q^{4} - 10q^{9} + 6q^{10} - 28q^{15} - 80q^{16} + 24q^{19} + 6q^{24} - 10q^{25} + 14q^{30} + 12q^{31} + 20q^{36} + 4q^{39} - 6q^{40} - 6q^{45} - 4q^{46} - 4q^{51} + 14q^{60} + 60q^{61} + 160q^{64} - 48q^{66} + 96q^{75} + 76q^{79} - 10q^{81} + 104q^{85} - 96q^{94} - 6q^{96} - 96q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1470, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1470, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)