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Properties

Label 1470.2.v
Level $1470$
Weight $2$
Character orbit 1470.v
Rep. character $\chi_{1470}(313,\cdot)$
Character field $\Q(\zeta_{12})$
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.v (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
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 160 1312
Cusp forms 1216 160 1056
Eisenstein series 256 0 256

Trace form

\( 160 q - 24 q^{5} + O(q^{10}) \) \( 160 q - 24 q^{5} - 12 q^{10} - 8 q^{11} - 8 q^{15} + 80 q^{16} - 24 q^{22} + 24 q^{23} + 24 q^{25} + 24 q^{26} + 16 q^{30} + 48 q^{31} - 12 q^{33} - 160 q^{36} + 8 q^{37} + 48 q^{38} + 80 q^{43} + 8 q^{46} + 24 q^{47} - 16 q^{51} + 80 q^{53} + 32 q^{57} + 44 q^{58} - 48 q^{61} - 64 q^{65} + 80 q^{67} + 96 q^{71} + 24 q^{73} + 48 q^{75} + 32 q^{78} - 24 q^{80} + 80 q^{81} - 48 q^{82} - 64 q^{85} + 32 q^{86} - 60 q^{87} - 12 q^{88} - 48 q^{92} - 16 q^{93} - 40 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(1470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)