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Properties

Label 1350.2.r
Level $1350$
Weight $2$
Character orbit 1350.r
Rep. character $\chi_{1350}(91,\cdot)$
Character field $\Q(\zeta_{15})$
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.r (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 240 q + 30 q^{4} - 8 q^{5} + O(q^{10}) \) \( 240 q + 30 q^{4} - 8 q^{5} - 4 q^{11} - 8 q^{14} + 30 q^{16} - 24 q^{17} + 2 q^{20} + 24 q^{25} - 96 q^{26} - 12 q^{29} - 12 q^{31} - 8 q^{35} + 24 q^{37} + 12 q^{38} - 16 q^{41} + 8 q^{44} - 26 q^{47} - 120 q^{49} + 12 q^{50} + 72 q^{53} - 8 q^{56} + 12 q^{58} - 18 q^{59} + 36 q^{62} - 60 q^{64} + 104 q^{65} + 18 q^{67} - 48 q^{68} - 24 q^{70} - 4 q^{71} + 80 q^{74} - 32 q^{77} + 12 q^{79} - 4 q^{80} - 48 q^{82} + 104 q^{83} + 12 q^{85} - 20 q^{86} + 188 q^{89} - 8 q^{95} + 12 q^{97} - 48 q^{98} + O(q^{100}) \)

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

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