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Properties

Label 360.4.br
Level $360$
Weight $4$
Character orbit 360.br
Rep. character $\chi_{360}(77,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $848$
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.br (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(288\)

Dimensions

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

Total New Old
Modular forms 880 880 0
Cusp forms 848 848 0
Eisenstein series 32 32 0

Trace form

\( 848 q - 6 q^{2} - 8 q^{6} - 4 q^{7} + O(q^{10}) \) \( 848 q - 6 q^{2} - 8 q^{6} - 4 q^{7} - 8 q^{10} + 50 q^{12} - 8 q^{15} - 4 q^{16} + 488 q^{18} - 6 q^{20} + 30 q^{22} - 12 q^{23} - 4 q^{25} - 264 q^{28} - 334 q^{30} - 8 q^{31} + 1374 q^{32} + 100 q^{33} - 472 q^{36} - 54 q^{38} - 2 q^{40} - 24 q^{41} + 110 q^{42} + 56 q^{46} - 12 q^{47} + 142 q^{48} - 6 q^{50} + 254 q^{52} + 984 q^{55} + 3936 q^{56} - 224 q^{57} - 34 q^{58} + 4078 q^{60} - 1380 q^{63} - 12 q^{65} + 4628 q^{66} - 390 q^{68} - 502 q^{70} - 3302 q^{72} - 16 q^{73} + 856 q^{76} + 4634 q^{78} - 1248 q^{81} - 40 q^{82} - 8328 q^{86} + 1172 q^{87} - 3114 q^{88} - 4782 q^{90} + 9456 q^{92} - 1512 q^{95} + 2332 q^{96} - 4 q^{97} + O(q^{100}) \)

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.