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Properties

Label 192.9.l
Level $192$
Weight $9$
Character orbit 192.l
Rep. character $\chi_{192}(79,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
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: \(288\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 528 64 464
Cusp forms 496 64 432
Eisenstein series 32 0 32

Trace form

\( 64 q + O(q^{10}) \) \( 64 q - 39552 q^{11} + 167552 q^{19} - 1691136 q^{23} - 2132352 q^{29} + 2415744 q^{35} - 4720512 q^{37} + 7244672 q^{43} + 52706752 q^{49} - 13862016 q^{51} - 5358720 q^{53} + 46326784 q^{55} - 44938752 q^{59} + 24476032 q^{61} + 29941632 q^{65} + 44244736 q^{67} - 8636544 q^{69} - 159664128 q^{71} - 12918528 q^{75} - 94964352 q^{77} - 306110016 q^{81} - 209328000 q^{83} + 106960000 q^{85} + 45401472 q^{91} - 86500224 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
192.9.l.a 192.l 16.f $64$ $78.217$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{9}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)