Properties

Label 192.2.f
Level $192$
Weight $2$
Character orbit 192.f
Rep. character $\chi_{192}(95,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $64$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 192.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(64\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 44 8 36
Cusp forms 20 8 12
Eisenstein series 24 0 24

Trace form

\( 8 q + O(q^{10}) \) \( 8 q + 8 q^{25} - 24 q^{33} - 24 q^{49} - 24 q^{57} - 16 q^{73} + 72 q^{81} + 64 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
192.2.f.a 192.f 24.f $4$ $1.533$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\zeta_{12}^{2}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}-3q^{9}+\cdots\)
192.2.f.b 192.f 24.f $4$ $1.533$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{12}q^{3}-\zeta_{12}^{3}q^{7}+3q^{9}-\zeta_{12}^{2}q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)