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Properties

Label 1350.2.bd
Level $1350$
Weight $2$
Character orbit 1350.bd
Rep. character $\chi_{1350}(17,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $480$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1350.bd (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1350, [\chi])\).

Total New Old
Modular forms 4512 480 4032
Cusp forms 4128 480 3648
Eisenstein series 384 0 384

Trace form

\( 480 q + O(q^{10}) \) \( 480 q - 60 q^{16} - 12 q^{20} - 24 q^{23} - 48 q^{25} + 24 q^{37} + 36 q^{38} + 48 q^{47} + 48 q^{50} + 24 q^{55} - 12 q^{58} + 60 q^{59} - 24 q^{65} + 12 q^{67} + 144 q^{68} + 432 q^{77} + 48 q^{82} + 60 q^{83} + 24 q^{85} - 24 q^{92} + 60 q^{95} + 36 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1350, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1350, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)