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Properties

Label 1350.2.l
Level $1350$
Weight $2$
Character orbit 1350.l
Rep. character $\chi_{1350}(151,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $342$
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.l (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 1692 342 1350
Cusp forms 1548 342 1206
Eisenstein series 144 0 144

Trace form

\( 342 q + 6 q^{6} - 3 q^{8} + 12 q^{9} + O(q^{10}) \) \( 342 q + 6 q^{6} - 3 q^{8} + 12 q^{9} + 9 q^{11} - 3 q^{12} + 6 q^{14} - 12 q^{17} + 6 q^{18} - 48 q^{21} - 9 q^{22} + 48 q^{23} - 36 q^{26} + 39 q^{27} + 42 q^{29} + 18 q^{31} + 39 q^{33} - 9 q^{34} - 6 q^{36} + 24 q^{38} + 42 q^{39} + 9 q^{41} + 24 q^{42} - 9 q^{43} + 6 q^{44} + 72 q^{47} + 6 q^{48} + 18 q^{49} + 84 q^{51} + 96 q^{53} + 6 q^{56} + 27 q^{57} + 54 q^{59} + 18 q^{61} - 24 q^{62} + 78 q^{63} - 171 q^{64} - 45 q^{67} + 24 q^{68} - 102 q^{69} + 24 q^{71} - 24 q^{72} - 18 q^{73} - 66 q^{74} + 18 q^{76} - 102 q^{77} + 60 q^{78} - 72 q^{79} + 96 q^{81} + 60 q^{83} + 9 q^{86} - 96 q^{87} + 18 q^{88} + 129 q^{89} - 18 q^{91} - 42 q^{92} + 42 q^{93} - 36 q^{94} + 6 q^{96} - 45 q^{97} - 15 q^{98} + 72 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)