Defining parameters
Level: | \( N \) | \(=\) | \( 184 = 2^{3} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 184.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(184))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 28 | 6 | 22 |
Cusp forms | 21 | 6 | 15 |
Eisenstein series | 7 | 0 | 7 |
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. |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(1\) |
\(+\) | \(-\) | \(-\) | \(2\) |
\(-\) | \(+\) | \(-\) | \(2\) |
\(-\) | \(-\) | \(+\) | \(1\) |
Plus space | \(+\) | \(2\) | |
Minus space | \(-\) | \(4\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(184))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 23 | |||||||
184.2.a.a | $1$ | $1.469$ | \(\Q\) | None | \(0\) | \(-1\) | \(-4\) | \(2\) | $-$ | $-$ | \(q-q^{3}-4q^{5}+2q^{7}-2q^{9}-4q^{11}+\cdots\) | |
184.2.a.b | $1$ | $1.469$ | \(\Q\) | None | \(0\) | \(-1\) | \(-2\) | \(-4\) | $+$ | $+$ | \(q-q^{3}-2q^{5}-4q^{7}-2q^{9}-2q^{11}+\cdots\) | |
184.2.a.c | $1$ | $1.469$ | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(4\) | $+$ | $-$ | \(q+4q^{7}-3q^{9}+6q^{11}-2q^{13}+6q^{17}+\cdots\) | |
184.2.a.d | $1$ | $1.469$ | \(\Q\) | None | \(0\) | \(3\) | \(0\) | \(-2\) | $+$ | $-$ | \(q+3q^{3}-2q^{7}+6q^{9}-5q^{13}-6q^{17}+\cdots\) | |
184.2.a.e | $2$ | $1.469$ | \(\Q(\sqrt{17}) \) | None | \(0\) | \(-1\) | \(4\) | \(0\) | $-$ | $+$ | \(q-\beta q^{3}+2q^{5}+(1+\beta )q^{9}+2\beta q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(184))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(184)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 2}\)