Properties

Label 192.11.t
Level $192$
Weight $11$
Character orbit 192.t
Rep. character $\chi_{192}(19,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1280$
Sturm bound $352$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 192.t (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(352\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(192, [\chi])\).

Total New Old
Modular forms 2576 1280 1296
Cusp forms 2544 1280 1264
Eisenstein series 32 0 32

Trace form

\( 1280 q + O(q^{10}) \) \( 1280 q + 17370576 q^{22} - 195998000 q^{26} + 71704560 q^{28} - 368701520 q^{32} - 331581360 q^{34} + 303212560 q^{38} - 1839744720 q^{40} - 1807214032 q^{44} + 4237196496 q^{50} - 1492836480 q^{51} - 2666806032 q^{52} - 382637520 q^{54} - 2854204928 q^{55} + 9214269680 q^{56} + 5996341760 q^{59} - 9129669408 q^{60} - 6642753504 q^{62} + 7557955680 q^{64} + 14444814240 q^{66} - 3393841792 q^{67} + 1090322400 q^{68} - 19585936608 q^{70} + 30291553280 q^{71} + 22843750160 q^{74} - 23834435328 q^{75} + 5915084240 q^{76} - 19595228400 q^{78} + 24897943040 q^{79} - 1325444304 q^{80} + 46496841040 q^{82} - 30573060560 q^{88} + 35898970080 q^{94} + O(q^{100}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

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

Decomposition of \(S_{11}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)