Defining parameters
Level: | \( N \) | \(=\) | \( 153 = 3^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 153.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(36\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(153))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 22 | 6 | 16 |
Cusp forms | 15 | 6 | 9 |
Eisenstein series | 7 | 0 | 7 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(17\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(-\) | $-$ | \(1\) |
\(-\) | \(+\) | $-$ | \(3\) |
\(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(2\) | |
Minus space | \(-\) | \(4\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(153))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 17 | |||||||
153.2.a.a | $1$ | $1.222$ | \(\Q\) | None | \(-2\) | \(0\) | \(-1\) | \(-2\) | $+$ | $+$ | \(q-2q^{2}+2q^{4}-q^{5}-2q^{7}+2q^{10}+\cdots\) | |
153.2.a.b | $1$ | $1.222$ | \(\Q\) | None | \(0\) | \(0\) | \(-3\) | \(-4\) | $-$ | $-$ | \(q-2q^{4}-3q^{5}-4q^{7}+3q^{11}-q^{13}+\cdots\) | |
153.2.a.c | $1$ | $1.222$ | \(\Q\) | None | \(1\) | \(0\) | \(2\) | \(4\) | $-$ | $+$ | \(q+q^{2}-q^{4}+2q^{5}+4q^{7}-3q^{8}+2q^{10}+\cdots\) | |
153.2.a.d | $1$ | $1.222$ | \(\Q\) | None | \(2\) | \(0\) | \(1\) | \(-2\) | $+$ | $-$ | \(q+2q^{2}+2q^{4}+q^{5}-2q^{7}+2q^{10}+\cdots\) | |
153.2.a.e | $2$ | $1.222$ | \(\Q(\sqrt{17}) \) | None | \(1\) | \(0\) | \(-3\) | \(0\) | $-$ | $+$ | \(q+\beta q^{2}+(2+\beta )q^{4}+(-1-\beta )q^{5}+(4+\cdots)q^{8}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(153))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(153)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)