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Properties

Label 288.8.v
Level $288$
Weight $8$
Character orbit 288.v
Rep. character $\chi_{288}(37,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $556$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 288.v (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(288, [\chi])\).

Total New Old
Modular forms 1360 564 796
Cusp forms 1328 556 772
Eisenstein series 32 8 24

Trace form

\( 556 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} + O(q^{10}) \) \( 556 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} + 12996 q^{10} + 4 q^{11} - 4 q^{13} - 26188 q^{14} - 10560 q^{16} - 4 q^{19} + 82004 q^{20} + 99776 q^{22} - 143412 q^{23} - 4 q^{25} - 363976 q^{26} - 195464 q^{28} + 4 q^{29} - 714992 q^{31} + 535664 q^{32} - 201072 q^{34} + 816508 q^{35} - 4 q^{37} + 1288180 q^{38} - 59992 q^{40} + 4 q^{41} + 366180 q^{43} - 1785068 q^{44} + 2715804 q^{46} - 663612 q^{50} - 8882220 q^{52} - 1815628 q^{53} + 4191004 q^{55} - 7082272 q^{56} + 2090592 q^{58} - 1835932 q^{59} + 4559772 q^{61} - 2601096 q^{62} - 5921608 q^{64} + 8 q^{65} - 388140 q^{67} - 9026600 q^{68} + 27840824 q^{70} - 12348700 q^{71} - 4 q^{73} + 10931444 q^{74} + 4707788 q^{76} - 11914444 q^{77} - 58141184 q^{80} - 33487444 q^{82} + 9565884 q^{83} + 312496 q^{85} + 54722560 q^{86} + 58234288 q^{88} + 4 q^{89} + 3406988 q^{91} - 26878104 q^{92} - 58858056 q^{94} + 54872008 q^{95} - 8 q^{97} - 5171944 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(288, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)