Properties

Label 192.1.h
Level $192$
Weight $1$
Character orbit 192.h
Rep. character $\chi_{192}(161,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 192.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(192, [\chi])\).

Total New Old
Modular forms 14 2 12
Cusp forms 2 2 0
Eisenstein series 12 0 12

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{9} - 2q^{25} - 2q^{49} + 4q^{57} + 4q^{73} + 2q^{81} - 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
192.1.h.a \(2\) \(0.096\) \(\Q(\sqrt{-1}) \) \(D_{2}\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{6}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-q^{9}+iq^{19}-q^{25}+iq^{27}+\cdots\)