Properties

Label 192.2.f
Level 192
Weight 2
Character orbit f
Rep. character \(\chi_{192}(95,\cdot)\)
Character field \(\Q\)
Dimension 8
Newforms 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: \(\Q\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(192, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
192.2.f.a \(4\) \(1.533\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}-3q^{9}+\cdots\)
192.2.f.b \(4\) \(1.533\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}^{3}q^{7}+3q^{9}-\zeta_{12}^{2}q^{13}+\cdots\)

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

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