Defining parameters
Level: | \( N \) | \(=\) | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 36.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(132\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(36))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 132 | 9 | 123 |
Cusp forms | 120 | 9 | 111 |
Eisenstein series | 12 | 0 | 12 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | Fricke | Dim |
---|---|---|---|
\(-\) | \(+\) | \(-\) | \(4\) |
\(-\) | \(-\) | \(+\) | \(5\) |
Plus space | \(+\) | \(5\) | |
Minus space | \(-\) | \(4\) |
Trace form
Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(36))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | |||||||
36.22.a.a | $1$ | $100.612$ | \(\Q\) | None | \(0\) | \(0\) | \(11268090\) | \(281914136\) | $-$ | $-$ | \(q+11268090q^{5}+281914136q^{7}+\cdots\) | |
36.22.a.b | $2$ | $100.612$ | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) | None | \(0\) | \(0\) | \(-28827900\) | \(509669728\) | $-$ | $-$ | \(q+(-14413950-5\beta )q^{5}+(254834864+\cdots)q^{7}+\cdots\) | |
36.22.a.c | $2$ | $100.612$ | \(\Q(\sqrt{2161}) \) | None | \(0\) | \(0\) | \(-13689324\) | \(-260508080\) | $-$ | $-$ | \(q+(-6844662-68\beta )q^{5}+(-130254040+\cdots)q^{7}+\cdots\) | |
36.22.a.d | $4$ | $100.612$ | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-574223440\) | $-$ | $+$ | \(q+\beta _{1}q^{5}+(-143555860-\beta _{3})q^{7}+\cdots\) |
Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(36))\) into lower level spaces
\( S_{22}^{\mathrm{old}}(\Gamma_0(36)) \simeq \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 2}\)