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Properties

Label 270.4.k
Level $270$
Weight $4$
Character orbit 270.k
Rep. character $\chi_{270}(31,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $216$
Sturm bound $216$

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Defining parameters

Level: \( N \) \(=\) \( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 270.k (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(216\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(270, [\chi])\).

Total New Old
Modular forms 996 216 780
Cusp forms 948 216 732
Eisenstein series 48 0 48

Trace form

\( 216 q - 12 q^{6} - 48 q^{8} - 96 q^{9} + O(q^{10}) \) \( 216 q - 12 q^{6} - 48 q^{8} - 96 q^{9} + 126 q^{11} + 24 q^{12} + 132 q^{14} - 408 q^{17} - 552 q^{18} - 120 q^{21} - 108 q^{22} + 1008 q^{23} + 2310 q^{27} + 1482 q^{29} - 1326 q^{33} + 540 q^{34} - 420 q^{35} + 168 q^{36} - 1272 q^{38} - 276 q^{39} - 2034 q^{41} + 1026 q^{43} + 330 q^{45} + 792 q^{47} - 594 q^{49} + 3036 q^{51} + 3816 q^{53} + 360 q^{54} + 528 q^{56} + 2250 q^{57} - 2724 q^{59} + 54 q^{61} - 2976 q^{62} - 2664 q^{63} - 6912 q^{64} - 3840 q^{65} - 8640 q^{66} + 2322 q^{67} - 912 q^{68} - 7500 q^{69} - 1080 q^{70} - 480 q^{71} - 864 q^{73} + 4344 q^{74} + 2160 q^{76} + 4344 q^{77} + 7104 q^{78} + 5616 q^{79} + 960 q^{80} + 9768 q^{81} + 12216 q^{83} + 2160 q^{84} + 4320 q^{85} + 5148 q^{86} + 2040 q^{87} + 864 q^{88} - 1410 q^{89} - 480 q^{90} + 1080 q^{91} - 2016 q^{92} - 11376 q^{93} - 3672 q^{94} - 6240 q^{95} - 1920 q^{96} + 54 q^{97} - 10716 q^{98} - 1632 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(270, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(270, [\chi])\) into lower level spaces

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