Defining parameters
Level: | \( N \) | \(=\) | \( 184 = 2^{3} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 184.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(184))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 124 | 28 | 96 |
Cusp forms | 116 | 28 | 88 |
Eisenstein series | 8 | 0 | 8 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(23\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(7\) |
\(+\) | \(-\) | $-$ | \(8\) |
\(-\) | \(+\) | $-$ | \(7\) |
\(-\) | \(-\) | $+$ | \(6\) |
Plus space | \(+\) | \(13\) | |
Minus space | \(-\) | \(15\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(184))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 23 | |||||||
184.6.a.a | $6$ | $29.511$ | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) | None | \(0\) | \(-15\) | \(-26\) | \(72\) | $-$ | $-$ | \(q+(-2-\beta _{3})q^{3}+(-4-\beta _{3}+\beta _{4})q^{5}+\cdots\) | |
184.6.a.b | $7$ | $29.511$ | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) | None | \(0\) | \(-23\) | \(-50\) | \(-146\) | $+$ | $+$ | \(q+(-3+\beta _{1})q^{3}+(-7+\beta _{2})q^{5}+(-22+\cdots)q^{7}+\cdots\) | |
184.6.a.c | $7$ | $29.511$ | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) | None | \(0\) | \(-15\) | \(174\) | \(-26\) | $-$ | $+$ | \(q+(-2-\beta _{1})q^{3}+(5^{2}-\beta _{2})q^{5}+(-3+\cdots)q^{7}+\cdots\) | |
184.6.a.d | $8$ | $29.511$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(13\) | \(0\) | \(148\) | $+$ | $-$ | \(q+(2-\beta _{1})q^{3}+\beta _{2}q^{5}+(18-\beta _{4})q^{7}+\cdots\) |
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(184))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_0(184)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 2}\)