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Properties

Label 192.9.q
Level $192$
Weight $9$
Character orbit 192.q
Rep. character $\chi_{192}(5,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $2032$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 192.q (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 192 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(192, [\chi])\).

Total New Old
Modular forms 2064 2064 0
Cusp forms 2032 2032 0
Eisenstein series 32 32 0

Trace form

\( 2032 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} + O(q^{10}) \) \( 2032 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 322288 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 7934328 q^{30} - 16 q^{34} - 7200408 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} + 35148512 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 45948128 q^{52} - 8 q^{54} + 92653552 q^{55} - 8 q^{57} + 101752544 q^{58} - 8 q^{60} - 16 q^{61} - 16 q^{63} - 96767920 q^{64} - 2056 q^{66} + 298817520 q^{67} - 8 q^{69} + 92889872 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} - 278781792 q^{76} - 299591552 q^{78} + 144406512 q^{79} - 8 q^{81} + 69799584 q^{82} - 689231320 q^{84} - 16 q^{85} - 8 q^{87} + 45587904 q^{88} + 873269992 q^{90} - 16 q^{91} + 52480 q^{93} + 310515728 q^{94} - 468840832 q^{96} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

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