Properties

Label 1470.2.y
Level $1470$
Weight $2$
Character orbit 1470.y
Rep. character $\chi_{1470}(263,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $320$
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.y (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 1472 320 1152
Cusp forms 1216 320 896
Eisenstein series 256 0 256

Trace form

\( 320q - 8q^{6} + O(q^{10}) \) \( 320q - 8q^{6} - 4q^{10} + 24q^{15} + 160q^{16} + 16q^{18} + 40q^{22} + 16q^{25} + 72q^{27} + 12q^{30} - 32q^{31} + 20q^{33} + 40q^{36} + 16q^{37} + 64q^{43} + 28q^{45} - 24q^{46} + 16q^{55} - 40q^{57} + 28q^{58} - 16q^{60} - 24q^{61} + 16q^{67} - 16q^{72} + 56q^{73} - 8q^{75} + 32q^{76} + 32q^{78} - 12q^{81} - 16q^{82} - 16q^{85} - 76q^{87} - 20q^{88} - 40q^{90} - 116q^{93} - 4q^{96} - 104q^{97} + O(q^{100}) \)

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

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