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Properties

Label 192.5.l
Level $192$
Weight $5$
Character orbit 192.l
Rep. character $\chi_{192}(79,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $32$
Newform subspaces $1$
Sturm bound $160$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 192.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(160\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(192, [\chi])\).

Total New Old
Modular forms 272 32 240
Cusp forms 240 32 208
Eisenstein series 32 0 32

Trace form

\( 32 q + O(q^{10}) \) \( 32 q + 192 q^{11} - 704 q^{19} + 2304 q^{23} - 1728 q^{29} + 5184 q^{35} + 3648 q^{37} - 1088 q^{43} + 10976 q^{49} + 4032 q^{51} + 960 q^{53} - 11776 q^{55} - 13056 q^{59} + 3776 q^{61} + 4032 q^{65} + 896 q^{67} - 9792 q^{69} + 39936 q^{71} + 1152 q^{75} + 9408 q^{77} - 23328 q^{81} - 24000 q^{83} - 11200 q^{85} - 30528 q^{91} + 5184 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
192.5.l.a 192.l 16.f $32$ $19.847$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{5}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)