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Properties

Label 360.4.bm
Level $360$
Weight $4$
Character orbit 360.bm
Rep. character $\chi_{360}(11,\cdot)$
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.bm (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

\( 288 q - 30 q^{6} + O(q^{10}) \) \( 288 q - 30 q^{6} - 266 q^{12} - 150 q^{14} + 116 q^{18} - 316 q^{24} - 3600 q^{25} - 264 q^{27} + 80 q^{30} + 464 q^{33} - 198 q^{34} + 786 q^{36} + 1740 q^{38} - 90 q^{40} - 120 q^{41} - 338 q^{42} - 36 q^{46} - 2444 q^{48} + 7056 q^{49} + 1400 q^{51} - 918 q^{52} - 92 q^{54} - 1974 q^{56} + 344 q^{57} + 594 q^{58} - 6120 q^{59} - 490 q^{60} + 1224 q^{64} + 904 q^{66} + 108 q^{68} - 1676 q^{72} - 5460 q^{74} + 558 q^{76} - 6078 q^{78} - 304 q^{81} - 1404 q^{82} - 7320 q^{83} + 658 q^{84} - 4158 q^{86} + 1170 q^{90} - 7980 q^{92} - 1350 q^{94} + 4598 q^{96} + 2656 q^{99} + O(q^{100}) \)

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

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