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Properties

Label 1350.4.j
Level $1350$
Weight $4$
Character orbit 1350.j
Rep. character $\chi_{1350}(199,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $108$
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.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1080\)

Dimensions

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

Total New Old
Modular forms 1692 108 1584
Cusp forms 1548 108 1440
Eisenstein series 144 0 144

Trace form

\( 108 q + 216 q^{4} + O(q^{10}) \) \( 108 q + 216 q^{4} - 60 q^{11} + 24 q^{14} - 864 q^{16} + 624 q^{26} + 1152 q^{29} - 72 q^{31} - 756 q^{41} - 480 q^{44} - 1008 q^{46} + 2250 q^{49} - 96 q^{56} + 1938 q^{59} - 36 q^{61} - 6912 q^{64} + 48 q^{71} + 2088 q^{74} - 1620 q^{79} - 3972 q^{86} - 10776 q^{89} - 2016 q^{91} + 1224 q^{94} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)