Defining parameters
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 76 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(76\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{76}(\Gamma_0(9))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 77 | 32 | 45 |
Cusp forms | 73 | 31 | 42 |
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 |
---|---|
\(+\) | \(13\) |
\(-\) | \(18\) |
Trace form
Decomposition of \(S_{76}^{\mathrm{new}}(\Gamma_0(9))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
9.76.a.a | $1$ | $320.606$ | \(\Q\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(97\!\cdots\!00\) | $+$ | \(q-2^{75}q^{4}+97488395945542679634576758400500q^{7}+\cdots\) | |
9.76.a.b | $6$ | $320.606$ | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) | None | \(-311057037486\) | \(0\) | \(-97\!\cdots\!60\) | \(-30\!\cdots\!88\) | $-$ | \(q+(-51842839581+\beta _{1})q^{2}+\cdots\) | |
9.76.a.c | $6$ | $320.606$ | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) | None | \(57080822040\) | \(0\) | \(38\!\cdots\!40\) | \(19\!\cdots\!00\) | $-$ | \(q+(9513470340-\beta _{1})q^{2}+\cdots\) | |
9.76.a.d | $6$ | $320.606$ | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) | None | \(59456439936\) | \(0\) | \(-15\!\cdots\!60\) | \(36\!\cdots\!48\) | $-$ | \(q+(9909406656+\beta _{1})q^{2}+\cdots\) | |
9.76.a.e | $12$ | $320.606$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-23\!\cdots\!60\) | $+$ | \(q+\beta _{1}q^{2}+(25358921809744727743012+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{76}^{\mathrm{old}}(\Gamma_0(9))\) into lower level spaces
\( S_{76}^{\mathrm{old}}(\Gamma_0(9)) \cong \) \(S_{76}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{76}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)