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Properties

Label 360.6.w
Level $360$
Weight $6$
Character orbit 360.w
Rep. character $\chi_{360}(163,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $296$
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.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Sturm bound: \(432\)

Dimensions

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

Total New Old
Modular forms 736 304 432
Cusp forms 704 296 408
Eisenstein series 32 8 24

Trace form

\( 296 q + 2 q^{2} + 248 q^{8} + O(q^{10}) \) \( 296 q + 2 q^{2} + 248 q^{8} + 566 q^{10} + 8 q^{11} - 1984 q^{16} - 400 q^{17} + 5460 q^{20} + 2436 q^{22} - 3120 q^{25} - 6836 q^{26} + 12412 q^{28} + 17612 q^{32} - 4772 q^{35} - 15236 q^{38} + 27796 q^{40} + 8 q^{41} - 1316 q^{43} - 34384 q^{46} + 29554 q^{50} + 112796 q^{52} - 138856 q^{56} + 30500 q^{58} - 128944 q^{62} + 17688 q^{65} + 89252 q^{67} + 115372 q^{68} + 239156 q^{70} - 25184 q^{73} - 255848 q^{76} + 208884 q^{80} - 101740 q^{82} - 126436 q^{83} + 178464 q^{86} + 439312 q^{88} + 329432 q^{91} - 230516 q^{92} - 51776 q^{97} - 448386 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{6}^{\mathrm{old}}(360, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)