Defining parameters
Level: | \( N \) | \(=\) | \( 176 = 2^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 176.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(176))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 30 | 5 | 25 |
Cusp forms | 19 | 5 | 14 |
Eisenstein series | 11 | 0 | 11 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(11\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(-\) | \(-\) | \(3\) |
\(-\) | \(+\) | \(-\) | \(1\) |
\(-\) | \(-\) | \(+\) | \(1\) |
Plus space | \(+\) | \(1\) | |
Minus space | \(-\) | \(4\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(176))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 11 | |||||||
176.2.a.a | $1$ | $1.405$ | \(\Q\) | None | \(0\) | \(-1\) | \(-3\) | \(-2\) | $-$ | $-$ | \(q-q^{3}-3q^{5}-2q^{7}-2q^{9}+q^{11}+\cdots\) | |
176.2.a.b | $1$ | $1.405$ | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(2\) | $-$ | $+$ | \(q+q^{3}+q^{5}+2q^{7}-2q^{9}-q^{11}+4q^{13}+\cdots\) | |
176.2.a.c | $1$ | $1.405$ | \(\Q\) | None | \(0\) | \(3\) | \(-3\) | \(2\) | $+$ | $-$ | \(q+3q^{3}-3q^{5}+2q^{7}+6q^{9}+q^{11}+\cdots\) | |
176.2.a.d | $2$ | $1.405$ | \(\Q(\sqrt{17}) \) | None | \(0\) | \(-1\) | \(3\) | \(2\) | $+$ | $-$ | \(q-\beta q^{3}+(2-\beta )q^{5}+2\beta q^{7}+(1+\beta )q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(176))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(176)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 2}\)