Defining parameters
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 74 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(74\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{74}(\Gamma_0(9))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 75 | 31 | 44 |
Cusp forms | 71 | 30 | 41 |
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 |
---|---|
\(+\) | \(12\) |
\(-\) | \(18\) |
Trace form
Decomposition of \(S_{74}^{\mathrm{new}}(\Gamma_0(9))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
9.74.a.a | $5$ | $303.736$ | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) | None | \(92089333488\) | \(0\) | \(-23\!\cdots\!50\) | \(-43\!\cdots\!08\) | $-$ | \(q+(18417866698+\beta _{1})q^{2}+\cdots\) | |
9.74.a.b | $6$ | $303.736$ | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) | None | \(-71256829788\) | \(0\) | \(15\!\cdots\!84\) | \(-91\!\cdots\!84\) | $-$ | \(q+(-11876138298-\beta _{1})q^{2}+\cdots\) | |
9.74.a.c | $7$ | $303.736$ | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) | None | \(-44202360450\) | \(0\) | \(22\!\cdots\!10\) | \(10\!\cdots\!52\) | $-$ | \(q+(-6314622921+\beta _{1})q^{2}+\cdots\) | |
9.74.a.d | $12$ | $303.736$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-13\!\cdots\!20\) | $+$ | \(q+\beta _{1}q^{2}+(4752100926420020816128+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{74}^{\mathrm{old}}(\Gamma_0(9))\) into lower level spaces
\( S_{74}^{\mathrm{old}}(\Gamma_0(9)) \cong \) \(S_{74}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{74}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)