Properties

Label 320.10.bf
Level $320$
Weight $10$
Character orbit 320.bf
Rep. character $\chi_{320}(29,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $3440$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 320.bf (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 320 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(320, [\chi])\).

Total New Old
Modular forms 3472 3472 0
Cusp forms 3440 3440 0
Eisenstein series 32 32 0

Trace form

\( 3440 q - 16 q^{4} - 8 q^{5} - 16 q^{6} - 16 q^{9} + O(q^{10}) \) \( 3440 q - 16 q^{4} - 8 q^{5} - 16 q^{6} - 16 q^{9} - 8 q^{10} - 16 q^{11} - 16 q^{14} - 8 q^{15} - 16 q^{16} - 16 q^{19} - 8 q^{20} - 16 q^{21} - 16 q^{24} - 8 q^{25} + 4211904 q^{26} - 16 q^{29} + 44263272 q^{30} - 16 q^{34} - 8 q^{35} + 221001424 q^{36} - 16 q^{39} + 97089632 q^{40} - 16 q^{41} - 16 q^{44} - 8 q^{45} - 16 q^{46} - 16 q^{49} - 182758304 q^{50} - 360057328 q^{51} + 646232240 q^{54} - 280217672 q^{55} + 348279440 q^{56} + 576150448 q^{59} - 230939432 q^{60} - 16 q^{61} + 1364809808 q^{64} - 16 q^{65} + 186001488 q^{66} - 16 q^{69} - 1869092072 q^{70} - 476202960 q^{71} + 3740885648 q^{74} - 2309166152 q^{75} - 888710992 q^{76} + 2269128656 q^{79} + 912355216 q^{80} - 16 q^{81} - 6148771904 q^{84} - 8 q^{85} - 16 q^{86} - 16 q^{89} - 8 q^{90} - 16 q^{91} - 12302565280 q^{94} - 16 q^{96} - 314944 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

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