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Properties

Label 192.9.t
Level $192$
Weight $9$
Character orbit 192.t
Rep. character $\chi_{192}(19,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1024$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 192.t (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
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 1024 1040
Cusp forms 2032 1024 1008
Eisenstein series 32 0 32

Trace form

\( 1024 q + O(q^{10}) \) \( 1024 q + 2136528 q^{22} + 6728400 q^{26} - 7230480 q^{28} + 9681840 q^{32} + 16553040 q^{34} - 32644080 q^{38} + 2303280 q^{40} - 45304272 q^{44} + 10290384 q^{50} - 55448064 q^{51} + 45948144 q^{52} - 19840464 q^{54} + 92653568 q^{55} - 113749776 q^{56} - 179755008 q^{59} + 163708128 q^{60} + 87863328 q^{62} - 96767904 q^{64} - 227315808 q^{66} + 74704384 q^{67} - 163729440 q^{68} + 92889888 q^{70} - 319328256 q^{71} + 340057872 q^{74} - 51674112 q^{75} - 39825968 q^{76} - 367979760 q^{78} + 144406528 q^{79} + 404319024 q^{80} - 69799600 q^{82} - 45587920 q^{88} - 310515744 q^{94} + O(q^{100}) \)

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.

Decomposition of \(S_{9}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)