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Properties

Label 1350.4.bd
Level $1350$
Weight $4$
Character orbit 1350.bd
Rep. character $\chi_{1350}(17,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1440$
Sturm bound $1080$

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Defining parameters

Level: \( N \) \(=\) \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1350.bd (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1350, [\chi])\).

Total New Old
Modular forms 13152 1440 11712
Cusp forms 12768 1440 11328
Eisenstein series 384 0 384

Trace form

\( 1440 q + O(q^{10}) \) \( 1440 q - 2880 q^{16} - 192 q^{20} - 312 q^{23} + 1152 q^{25} + 288 q^{37} - 72 q^{38} - 3444 q^{47} - 672 q^{50} + 1584 q^{55} + 504 q^{58} + 9960 q^{59} + 696 q^{65} + 1224 q^{67} - 4608 q^{68} - 22896 q^{77} - 3744 q^{82} - 2820 q^{83} - 1656 q^{85} - 1248 q^{92} - 3540 q^{95} + 1512 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1350, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1350, [\chi])\) into lower level spaces

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