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Properties

Label 192.8.s
Level $192$
Weight $8$
Character orbit 192.s
Rep. character $\chi_{192}(11,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1776$
Sturm bound $256$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 192.s (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 192 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(256\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(192, [\chi])\).

Total New Old
Modular forms 1808 1808 0
Cusp forms 1776 1776 0
Eisenstein series 32 32 0

Trace form

\( 1776 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} + O(q^{10}) \) \( 1776 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} + 598032 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} + 1739912 q^{30} - 32 q^{31} - 16 q^{34} - 4069528 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} + 3858912 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} - 10204960 q^{52} - 8 q^{54} - 8382032 q^{55} - 8 q^{57} + 20716256 q^{58} - 8 q^{60} - 16 q^{61} - 22837168 q^{64} - 1032 q^{66} - 6210192 q^{67} - 8 q^{69} + 35990288 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} - 68150112 q^{76} + 39347584 q^{78} + 523728 q^{79} - 8 q^{81} - 49314656 q^{82} + 17056808 q^{84} - 16 q^{85} - 8 q^{87} + 52517824 q^{88} + 31733992 q^{90} - 16 q^{91} - 17504 q^{93} - 74691568 q^{94} - 112868992 q^{96} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

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