Defining parameters
Level: | \( N \) | \(=\) | \( 90 = 2 \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 90.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(36\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(90))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 26 | 3 | 23 |
Cusp forms | 11 | 3 | 8 |
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.
\(2\) | \(3\) | \(5\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(-\) | \(-\) | \(1\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(1\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(1\) |
Plus space | \(+\) | \(0\) | ||
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(90))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | 5 | |||||||
90.2.a.a | $1$ | $0.719$ | \(\Q\) | None | \(-1\) | \(0\) | \(1\) | \(2\) | $+$ | $+$ | $-$ | \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\) | |
90.2.a.b | $1$ | $0.719$ | \(\Q\) | None | \(1\) | \(0\) | \(-1\) | \(2\) | $-$ | $+$ | $+$ | \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\) | |
90.2.a.c | $1$ | $0.719$ | \(\Q\) | None | \(1\) | \(0\) | \(1\) | \(-4\) | $-$ | $-$ | $-$ | \(q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(90))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(90)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 2}\)