Defining parameters
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 94 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(94\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{94}(\Gamma_0(9))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 95 | 39 | 56 |
Cusp forms | 91 | 38 | 53 |
Eisenstein series | 4 | 1 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | Dim |
---|---|
\(+\) | \(15\) |
\(-\) | \(23\) |
Trace form
Decomposition of \(S_{94}^{\mathrm{new}}(\Gamma_0(9))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
9.94.a.a | $1$ | $492.953$ | \(\Q\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(36\!\cdots\!60\) | $+$ | \(q-2^{93}q^{4}+\cdots\) | |
9.94.a.b | $7$ | $492.953$ | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) | None | \(-43\!\cdots\!92\) | \(0\) | \(24\!\cdots\!50\) | \(-92\!\cdots\!08\) | $-$ | \(q+(-6247918101970-\beta _{1})q^{2}+\cdots\) | |
9.94.a.c | $8$ | $492.953$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(40\!\cdots\!26\) | \(0\) | \(-38\!\cdots\!16\) | \(55\!\cdots\!48\) | $-$ | \(q+(5118281421091+\beta _{1})q^{2}+\cdots\) | |
9.94.a.d | $8$ | $492.953$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(11\!\cdots\!24\) | \(0\) | \(46\!\cdots\!60\) | \(16\!\cdots\!12\) | $-$ | \(q+(14611668279566+\beta _{1})q^{2}+\cdots\) | |
9.94.a.e | $14$ | $492.953$ | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-76\!\cdots\!80\) | $+$ | \(q+\beta _{1}q^{2}+(6625177926194454250944644231+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{94}^{\mathrm{old}}(\Gamma_0(9))\) into lower level spaces
\( S_{94}^{\mathrm{old}}(\Gamma_0(9)) \cong \) \(S_{94}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{94}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)