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Properties

Label 192.4.k
Level $192$
Weight $4$
Character orbit 192.k
Rep. character $\chi_{192}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $44$
Newform subspaces $1$
Sturm bound $128$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 192.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(128\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(192, [\chi])\).

Total New Old
Modular forms 208 52 156
Cusp forms 176 44 132
Eisenstein series 32 8 24

Trace form

\( 44 q + 2 q^{3} + 8 q^{7} + O(q^{10}) \) \( 44 q + 2 q^{3} + 8 q^{7} - 4 q^{13} - 20 q^{19} - 56 q^{21} + 134 q^{27} - 4 q^{33} - 4 q^{37} - 596 q^{39} + 436 q^{43} - 252 q^{45} + 972 q^{49} + 648 q^{51} - 280 q^{55} - 916 q^{61} + 1636 q^{67} + 52 q^{69} - 1454 q^{75} - 4 q^{81} + 736 q^{85} - 1284 q^{87} - 424 q^{91} - 2084 q^{93} - 8 q^{97} - 1196 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
192.4.k.a 192.k 48.k $44$ $11.328$ None \(0\) \(2\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

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