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Properties

Label 192.4.a
Level $192$
Weight $4$
Character orbit 192.a
Rep. character $\chi_{192}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $12$
Sturm bound $128$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 192.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(128\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(192))\).

Total New Old
Modular forms 108 12 96
Cusp forms 84 12 72
Eisenstein series 24 0 24

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
\(+\)\(+\)$+$\(3\)
\(+\)\(-\)$-$\(2\)
\(-\)\(+\)$-$\(3\)
\(-\)\(-\)$+$\(4\)
Plus space\(+\)\(7\)
Minus space\(-\)\(5\)

Trace form

\( 12 q + 108 q^{9} + O(q^{10}) \) \( 12 q + 108 q^{9} - 72 q^{13} + 104 q^{17} + 120 q^{21} + 212 q^{25} + 400 q^{29} + 520 q^{37} - 472 q^{41} + 588 q^{49} - 752 q^{53} + 1992 q^{61} - 1536 q^{65} + 528 q^{69} - 296 q^{73} - 5408 q^{77} + 972 q^{81} - 2592 q^{85} + 88 q^{89} + 1848 q^{93} - 328 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(192))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
192.4.a.a 192.a 1.a $1$ $11.328$ \(\Q\) None \(0\) \(-3\) \(-14\) \(-24\) $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-14q^{5}-24q^{7}+9q^{9}+28q^{11}+\cdots\)
192.4.a.b 192.a 1.a $1$ $11.328$ \(\Q\) None \(0\) \(-3\) \(-10\) \(4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-10q^{5}+4q^{7}+9q^{9}+20q^{11}+\cdots\)
192.4.a.c 192.a 1.a $1$ $11.328$ \(\Q\) None \(0\) \(-3\) \(-6\) \(16\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-6q^{5}+2^{4}q^{7}+9q^{9}+12q^{11}+\cdots\)
192.4.a.d 192.a 1.a $1$ $11.328$ \(\Q\) None \(0\) \(-3\) \(-2\) \(12\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{5}+12q^{7}+9q^{9}-60q^{11}+\cdots\)
192.4.a.e 192.a 1.a $1$ $11.328$ \(\Q\) None \(0\) \(-3\) \(14\) \(-36\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+14q^{5}-6^{2}q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
192.4.a.f 192.a 1.a $1$ $11.328$ \(\Q\) None \(0\) \(-3\) \(18\) \(8\) $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+18q^{5}+8q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)
192.4.a.g 192.a 1.a $1$ $11.328$ \(\Q\) None \(0\) \(3\) \(-14\) \(24\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-14q^{5}+24q^{7}+9q^{9}-28q^{11}+\cdots\)
192.4.a.h 192.a 1.a $1$ $11.328$ \(\Q\) None \(0\) \(3\) \(-10\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-10q^{5}-4q^{7}+9q^{9}-20q^{11}+\cdots\)
192.4.a.i 192.a 1.a $1$ $11.328$ \(\Q\) None \(0\) \(3\) \(-6\) \(-16\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-6q^{5}-2^{4}q^{7}+9q^{9}-12q^{11}+\cdots\)
192.4.a.j 192.a 1.a $1$ $11.328$ \(\Q\) None \(0\) \(3\) \(-2\) \(-12\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-2q^{5}-12q^{7}+9q^{9}+60q^{11}+\cdots\)
192.4.a.k 192.a 1.a $1$ $11.328$ \(\Q\) None \(0\) \(3\) \(14\) \(36\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+14q^{5}+6^{2}q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)
192.4.a.l 192.a 1.a $1$ $11.328$ \(\Q\) None \(0\) \(3\) \(18\) \(-8\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+18q^{5}-8q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(192))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(192)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 2}\)