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Properties

Label 1350.4.bf
Level $1350$
Weight $4$
Character orbit 1350.bf
Rep. character $\chi_{1350}(79,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $6480$
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.bf (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 675 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(1080\)

Dimensions

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

Total New Old
Modular forms 19536 6480 13056
Cusp forms 19344 6480 12864
Eisenstein series 192 0 192

Trace form

\( 6480 q + 96 q^{5} + O(q^{10}) \) \( 6480 q + 96 q^{5} - 732 q^{15} - 192 q^{20} + 288 q^{21} + 1728 q^{25} + 7488 q^{26} + 504 q^{30} + 216 q^{31} - 828 q^{35} + 1536 q^{36} - 840 q^{39} - 528 q^{44} - 4056 q^{45} - 5700 q^{47} - 960 q^{48} - 1464 q^{50} + 1656 q^{54} - 2988 q^{59} + 1008 q^{60} - 51840 q^{64} + 4848 q^{65} - 18360 q^{67} - 642 q^{75} - 32640 q^{77} + 684 q^{81} - 12450 q^{87} - 6888 q^{89} + 780 q^{90} - 6240 q^{92} + 4122 q^{95} + 60 q^{99} + O(q^{100}) \)

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

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