Properties

Label 1470.2.bt
Level $1470$
Weight $2$
Character orbit 1470.bt
Rep. character $\chi_{1470}(23,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $2688$
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.bt (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 735 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 8256 2688 5568
Cusp forms 7872 2688 5184
Eisenstein series 384 0 384

Trace form

\( 2688q + 20q^{6} - 4q^{7} + O(q^{10}) \) \( 2688q + 20q^{6} - 4q^{7} - 4q^{10} + 24q^{15} - 224q^{16} - 12q^{21} - 20q^{22} + 72q^{27} - 4q^{28} + 12q^{30} - 32q^{31} + 20q^{33} - 20q^{36} - 72q^{42} + 64q^{43} + 140q^{45} + 312q^{46} + 16q^{55} - 92q^{57} + 224q^{58} + 200q^{61} + 88q^{63} + 16q^{67} + 40q^{70} + 56q^{73} - 92q^{75} + 32q^{76} + 32q^{81} - 16q^{82} - 48q^{85} - 76q^{87} - 4q^{88} - 124q^{90} - 176q^{91} + 88q^{93} - 4q^{96} - 104q^{97} + O(q^{100}) \)

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

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