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Properties

Label 1350.3.t
Level $1350$
Weight $3$
Character orbit 1350.t
Rep. character $\chi_{1350}(101,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $684$
Sturm bound $810$

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Defining parameters

Level: \( N \) \(=\) \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1350.t (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(810\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1350, [\chi])\).

Total New Old
Modular forms 3312 684 2628
Cusp forms 3168 684 2484
Eisenstein series 144 0 144

Trace form

\( 684 q - 12 q^{6} + 12 q^{9} + O(q^{10}) \) \( 684 q - 12 q^{6} + 12 q^{9} + 54 q^{11} - 12 q^{12} + 36 q^{14} - 48 q^{18} + 132 q^{21} + 36 q^{22} - 36 q^{23} - 42 q^{27} + 72 q^{29} + 90 q^{31} + 192 q^{33} - 72 q^{34} - 168 q^{36} - 36 q^{38} - 102 q^{39} + 54 q^{41} - 48 q^{42} + 90 q^{43} - 54 q^{47} + 24 q^{48} - 72 q^{49} + 210 q^{51} + 324 q^{54} + 72 q^{56} + 540 q^{57} + 648 q^{59} + 144 q^{61} + 402 q^{63} + 2736 q^{64} - 432 q^{66} + 342 q^{67} + 36 q^{68} + 150 q^{69} - 648 q^{71} + 192 q^{72} + 126 q^{73} + 72 q^{74} - 72 q^{76} - 342 q^{77} + 96 q^{78} + 72 q^{79} - 228 q^{81} + 234 q^{83} - 216 q^{84} + 756 q^{86} - 402 q^{87} + 144 q^{88} + 2268 q^{89} - 198 q^{91} - 180 q^{92} + 1086 q^{93} - 504 q^{94} + 96 q^{96} - 522 q^{97} + 648 q^{98} - 90 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1350, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(1350, [\chi])\) into lower level spaces

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