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Properties

Label 360.4.bf
Level $360$
Weight $4$
Character orbit 360.bf
Rep. character $\chi_{360}(61,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $288$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 360.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(360, [\chi])\).

Total New Old
Modular forms 440 288 152
Cusp forms 424 288 136
Eisenstein series 16 0 16

Trace form

\( 288 q + 30 q^{6} + 12 q^{8} + O(q^{10}) \) \( 288 q + 30 q^{6} + 12 q^{8} + 46 q^{12} + 50 q^{14} + 116 q^{18} - 552 q^{23} + 684 q^{24} + 3600 q^{25} - 1048 q^{26} + 80 q^{30} - 980 q^{32} - 464 q^{33} - 198 q^{34} + 994 q^{36} + 580 q^{38} - 600 q^{39} - 90 q^{40} + 40 q^{41} + 1018 q^{42} + 356 q^{44} + 36 q^{46} + 1880 q^{47} - 460 q^{48} - 7056 q^{49} + 918 q^{52} + 312 q^{54} - 342 q^{56} + 344 q^{57} - 594 q^{58} + 490 q^{60} - 284 q^{62} - 80 q^{63} - 144 q^{64} - 1380 q^{66} - 3104 q^{68} - 4120 q^{72} - 1624 q^{74} - 558 q^{76} - 2438 q^{78} - 2320 q^{80} - 1536 q^{81} - 1404 q^{82} + 2798 q^{84} + 1646 q^{86} - 8112 q^{87} + 848 q^{89} + 1170 q^{90} - 3276 q^{92} - 1350 q^{94} + 3040 q^{95} + 1306 q^{96} + 11640 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(360, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(360, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)