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Properties

Label 1350.2.bi
Level $1350$
Weight $2$
Character orbit 1350.bi
Rep. character $\chi_{1350}(23,\cdot)$
Character field $\Q(\zeta_{180})$
Dimension $4320$
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.bi (of order \(180\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 675 \)
Character field: \(\Q(\zeta_{180})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 13152 4320 8832
Cusp forms 12768 4320 8448
Eisenstein series 384 0 384

Trace form

\( 4320 q + O(q^{10}) \) \( 4320 q + 24 q^{20} - 24 q^{23} + 144 q^{25} - 12 q^{27} + 72 q^{30} + 12 q^{33} + 108 q^{35} + 36 q^{38} + 48 q^{42} + 60 q^{45} + 48 q^{47} + 12 q^{48} + 48 q^{50} + 36 q^{57} + 60 q^{59} - 84 q^{63} - 24 q^{65} + 72 q^{67} + 144 q^{68} + 48 q^{72} + 36 q^{75} - 720 q^{77} - 24 q^{78} + 60 q^{83} + 252 q^{87} + 48 q^{92} + 96 q^{93} + 60 q^{95} + 72 q^{97} + O(q^{100}) \)

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

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