Properties

Label 192.2.a
Level $192$
Weight $2$
Character orbit 192.a
Rep. character $\chi_{192}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $4$
Sturm bound $64$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 192.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(64\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(192))\).

Total New Old
Modular forms 44 4 40
Cusp forms 21 4 17
Eisenstein series 23 0 23

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)FrickeDim
\(+\)\(+\)$+$\(1\)
\(+\)\(-\)$-$\(2\)
\(-\)\(+\)$-$\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(3\)

Trace form

\( 4 q + 4 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{9} + 8 q^{13} - 8 q^{17} + 8 q^{21} - 4 q^{25} - 16 q^{29} - 8 q^{37} - 8 q^{41} + 4 q^{49} - 16 q^{53} - 8 q^{61} - 16 q^{69} + 8 q^{73} + 32 q^{77} + 4 q^{81} + 32 q^{85} + 8 q^{89} + 8 q^{93} - 24 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(192))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
192.2.a.a 192.a 1.a $1$ $1.533$ \(\Q\) None 96.2.a.a \(0\) \(-1\) \(-2\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
192.2.a.b 192.a 1.a $1$ $1.533$ \(\Q\) None 24.2.a.a \(0\) \(-1\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
192.2.a.c 192.a 1.a $1$ $1.533$ \(\Q\) None 96.2.a.a \(0\) \(1\) \(-2\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
192.2.a.d 192.a 1.a $1$ $1.533$ \(\Q\) None 24.2.a.a \(0\) \(1\) \(2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(192))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(192)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 2}\)