Defining parameters
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(99))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 16 | 4 | 12 |
Cusp forms | 9 | 4 | 5 |
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.
\(3\) | \(11\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(1\) |
\(+\) | \(-\) | \(-\) | \(1\) |
\(-\) | \(+\) | \(-\) | \(2\) |
Plus space | \(+\) | \(1\) | |
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(99))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 11 | |||||||
99.2.a.a | $1$ | $0.791$ | \(\Q\) | None | \(-1\) | \(0\) | \(-4\) | \(-2\) | $+$ | $+$ | \(q-q^{2}-q^{4}-4q^{5}-2q^{7}+3q^{8}+4q^{10}+\cdots\) | |
99.2.a.b | $1$ | $0.791$ | \(\Q\) | None | \(-1\) | \(0\) | \(2\) | \(4\) | $-$ | $+$ | \(q-q^{2}-q^{4}+2q^{5}+4q^{7}+3q^{8}-2q^{10}+\cdots\) | |
99.2.a.c | $1$ | $0.791$ | \(\Q\) | None | \(1\) | \(0\) | \(4\) | \(-2\) | $+$ | $-$ | \(q+q^{2}-q^{4}+4q^{5}-2q^{7}-3q^{8}+4q^{10}+\cdots\) | |
99.2.a.d | $1$ | $0.791$ | \(\Q\) | None | \(2\) | \(0\) | \(-1\) | \(-2\) | $-$ | $+$ | \(q+2q^{2}+2q^{4}-q^{5}-2q^{7}-2q^{10}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(99))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(99)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 2}\)