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Properties

Label 360.4.bo
Level $360$
Weight $4$
Character orbit 360.bo
Rep. character $\chi_{360}(43,\cdot)$
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.bo (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

\( 848 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} + O(q^{10}) \) \( 848 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 58 q^{12} - 4 q^{16} - 16 q^{17} - 496 q^{18} + 254 q^{20} + 30 q^{22} - 4 q^{25} + 528 q^{26} - 8 q^{27} + 248 q^{28} + 326 q^{30} + 458 q^{32} + 100 q^{33} - 16 q^{35} - 56 q^{36} - 1190 q^{38} - 2 q^{40} - 8 q^{41} - 786 q^{42} - 4 q^{43} - 88 q^{46} + 250 q^{48} - 1242 q^{50} - 16 q^{51} + 254 q^{52} - 1320 q^{56} + 208 q^{57} + 30 q^{58} + 4334 q^{60} + 3140 q^{62} - 4 q^{65} - 1964 q^{66} - 4 q^{67} - 550 q^{68} + 498 q^{70} - 586 q^{72} - 16 q^{73} + 6600 q^{75} - 864 q^{76} - 5690 q^{78} - 388 q^{80} + 1216 q^{81} + 24 q^{82} - 4 q^{83} + 2768 q^{86} + 1062 q^{88} + 10606 q^{90} - 32 q^{91} - 2900 q^{92} + 1740 q^{96} - 4 q^{97} + 3916 q^{98} + O(q^{100}) \)

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.