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Properties

Label 1350.2.z
Level $1350$
Weight $2$
Character orbit 1350.z
Rep. character $\chi_{1350}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $240$
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.z (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 2256 240 2016
Cusp forms 2064 240 1824
Eisenstein series 192 0 192

Trace form

\( 240 q - 30 q^{4} + 8 q^{5} + O(q^{10}) \) \( 240 q - 30 q^{4} + 8 q^{5} + 4 q^{11} - 8 q^{14} + 30 q^{16} + 2 q^{20} + 24 q^{25} + 96 q^{26} - 12 q^{29} + 12 q^{31} + 32 q^{35} + 16 q^{41} + 8 q^{44} + 50 q^{47} + 120 q^{49} + 4 q^{50} + 24 q^{55} + 8 q^{56} - 18 q^{59} + 60 q^{62} + 60 q^{64} + 64 q^{65} - 30 q^{67} + 24 q^{70} - 76 q^{71} + 80 q^{74} - 80 q^{77} + 12 q^{79} + 4 q^{80} + 140 q^{83} + 12 q^{85} + 20 q^{86} + 28 q^{89} + 40 q^{92} - 36 q^{95} + O(q^{100}) \)

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

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