Defining parameters
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(552))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 104 | 10 | 94 |
Cusp forms | 89 | 10 | 79 |
Eisenstein series | 15 | 0 | 15 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(23\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(+\) | \(-\) | $-$ | \(2\) |
\(+\) | \(-\) | \(+\) | $-$ | \(3\) |
\(-\) | \(+\) | \(-\) | $+$ | \(1\) |
\(-\) | \(-\) | \(+\) | $+$ | \(1\) |
\(-\) | \(-\) | \(-\) | $-$ | \(2\) |
Plus space | \(+\) | \(3\) | ||
Minus space | \(-\) | \(7\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(552))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | 23 | |||||||
552.2.a.a | $1$ | $4.408$ | \(\Q\) | None | \(0\) | \(-1\) | \(-2\) | \(2\) | $+$ | $+$ | $+$ | \(q-q^{3}-2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots\) | |
552.2.a.b | $1$ | $4.408$ | \(\Q\) | None | \(0\) | \(-1\) | \(0\) | \(-2\) | $+$ | $+$ | $-$ | \(q-q^{3}-2q^{7}+q^{9}+2q^{13}+8q^{17}+\cdots\) | |
552.2.a.c | $1$ | $4.408$ | \(\Q\) | None | \(0\) | \(-1\) | \(2\) | \(-4\) | $-$ | $+$ | $-$ | \(q-q^{3}+2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\) | |
552.2.a.d | $1$ | $4.408$ | \(\Q\) | None | \(0\) | \(-1\) | \(4\) | \(2\) | $+$ | $+$ | $-$ | \(q-q^{3}+4q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\) | |
552.2.a.e | $1$ | $4.408$ | \(\Q\) | None | \(0\) | \(1\) | \(-2\) | \(-4\) | $-$ | $-$ | $+$ | \(q+q^{3}-2q^{5}-4q^{7}+q^{9}-2q^{13}+\cdots\) | |
552.2.a.f | $2$ | $4.408$ | \(\Q(\sqrt{5}) \) | None | \(0\) | \(2\) | \(2\) | \(4\) | $-$ | $-$ | $-$ | \(q+q^{3}+(1+\beta )q^{5}+2q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\) | |
552.2.a.g | $3$ | $4.408$ | 3.3.148.1 | None | \(0\) | \(3\) | \(0\) | \(2\) | $+$ | $-$ | $+$ | \(q+q^{3}+\beta _{2}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(552))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(552)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 2}\)