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.
\(2\) | \(3\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||
\(+\) | \(+\) | \(+\) | \(10\) | \(1\) | \(9\) | \(5\) | \(1\) | \(4\) | \(5\) | \(0\) | \(5\) | |||
\(+\) | \(-\) | \(-\) | \(12\) | \(2\) | \(10\) | \(6\) | \(2\) | \(4\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(+\) | \(-\) | \(12\) | \(1\) | \(11\) | \(6\) | \(1\) | \(5\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(-\) | \(+\) | \(10\) | \(0\) | \(10\) | \(4\) | \(0\) | \(4\) | \(6\) | \(0\) | \(6\) | |||
Plus space | \(+\) | \(20\) | \(1\) | \(19\) | \(9\) | \(1\) | \(8\) | \(11\) | \(0\) | \(11\) | ||||
Minus space | \(-\) | \(24\) | \(3\) | \(21\) | \(12\) | \(3\) | \(9\) | \(12\) | \(0\) | \(12\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(192))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | |||||||
192.2.a.a | $1$ | $1.533$ | \(\Q\) | None | \(0\) | \(-1\) | \(-2\) | \(-4\) | $+$ | $+$ | \(q-q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\) | |
192.2.a.b | $1$ | $1.533$ | \(\Q\) | None | \(0\) | \(-1\) | \(2\) | \(0\) | $-$ | $+$ | \(q-q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\) | |
192.2.a.c | $1$ | $1.533$ | \(\Q\) | None | \(0\) | \(1\) | \(-2\) | \(4\) | $+$ | $-$ | \(q+q^{3}-2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\) | |
192.2.a.d | $1$ | $1.533$ | \(\Q\) | None | \(0\) | \(1\) | \(2\) | \(0\) | $+$ | $-$ | \(q+q^{3}+2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(192))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(192)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 2}\)