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Properties

Label 360.4.w
Level $360$
Weight $4$
Character orbit 360.w
Rep. character $\chi_{360}(163,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $176$
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.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Sturm bound: \(288\)

Dimensions

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

Total New Old
Modular forms 448 184 264
Cusp forms 416 176 240
Eisenstein series 32 8 24

Trace form

\( 176 q + 2 q^{2} - 40 q^{8} + O(q^{10}) \) \( 176 q + 2 q^{2} - 40 q^{8} - 74 q^{10} + 8 q^{11} - 192 q^{16} + 56 q^{17} - 60 q^{20} - 364 q^{22} + 40 q^{25} + 460 q^{26} - 244 q^{28} - 628 q^{32} - 452 q^{35} - 596 q^{38} + 276 q^{40} + 8 q^{41} + 860 q^{43} + 368 q^{46} - 446 q^{50} + 92 q^{52} + 248 q^{56} + 20 q^{58} + 272 q^{62} + 528 q^{65} - 1852 q^{67} + 268 q^{68} - 1884 q^{70} - 744 q^{73} + 568 q^{76} + 564 q^{80} - 1756 q^{82} + 2684 q^{83} + 1440 q^{86} - 3056 q^{88} - 1704 q^{91} - 932 q^{92} + 2392 q^{97} - 3762 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{4}^{\mathrm{old}}(360, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)