Properties

Label 192.2.r
Level $192$
Weight $2$
Character orbit 192.r
Rep. character $\chi_{192}(13,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $128$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 192.r (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(192, [\chi])\).

Total New Old
Modular forms 272 128 144
Cusp forms 240 128 112
Eisenstein series 32 0 32

Trace form

\( 128q + O(q^{10}) \) \( 128q - 16q^{22} - 80q^{26} - 80q^{28} - 80q^{32} - 80q^{34} - 80q^{38} - 80q^{40} - 16q^{44} + 48q^{50} - 32q^{51} + 48q^{52} + 16q^{54} - 64q^{55} + 112q^{56} - 128q^{59} + 96q^{60} + 96q^{62} - 32q^{63} + 96q^{64} + 96q^{66} - 32q^{67} + 96q^{68} + 96q^{70} - 128q^{71} + 112q^{74} - 64q^{75} + 16q^{76} + 48q^{78} - 32q^{79} + 48q^{80} - 80q^{82} - 80q^{88} - 96q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
192.2.r.a \(128\) \(1.533\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

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