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Properties

Label 360.6.br
Level $360$
Weight $6$
Character orbit 360.br
Rep. character $\chi_{360}(77,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1424$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 360.br (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(360, [\chi])\).

Total New Old
Modular forms 1456 1456 0
Cusp forms 1424 1424 0
Eisenstein series 32 32 0

Trace form

\( 1424 q - 6 q^{2} - 8 q^{6} - 4 q^{7} + O(q^{10}) \) \( 1424 q - 6 q^{2} - 8 q^{6} - 4 q^{7} - 8 q^{10} + 482 q^{12} - 8 q^{15} - 4 q^{16} - 7528 q^{18} - 6 q^{20} + 126 q^{22} - 12 q^{23} - 4 q^{25} - 4104 q^{28} + 22466 q^{30} - 8 q^{31} - 14466 q^{32} + 964 q^{33} + 21416 q^{36} - 198 q^{38} - 2 q^{40} - 24 q^{41} + 95486 q^{42} - 53896 q^{46} - 12 q^{47} - 49970 q^{48} - 6 q^{50} + 4094 q^{52} + 24984 q^{55} - 143232 q^{56} - 1952 q^{57} - 130 q^{58} - 246242 q^{60} - 67236 q^{63} - 12 q^{65} + 96116 q^{66} - 6150 q^{68} - 12502 q^{70} + 14074 q^{72} - 16 q^{73} - 54440 q^{76} - 633430 q^{78} + 89664 q^{81} - 136 q^{82} + 556728 q^{86} + 281204 q^{87} + 114006 q^{88} + 1129218 q^{90} - 690960 q^{92} - 37512 q^{95} - 277508 q^{96} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(360, [\chi])\) into newform subspaces

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