Defining parameters
Level: | \( N \) | \(=\) | \( 176 = 2^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 176.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 44 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(176, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 30 | 6 | 24 |
Cusp forms | 18 | 6 | 12 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(176, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
176.2.e.a | $2$ | $1.405$ | \(\Q(\sqrt{-11}) \) | \(\Q(\sqrt{-11}) \) | \(0\) | \(0\) | \(6\) | \(0\) | \(q-\beta q^{3}+3q^{5}-8q^{9}+\beta q^{11}-3\beta q^{15}+\cdots\) |
176.2.e.b | $4$ | $1.405$ | \(\Q(\sqrt{-3}, \sqrt{-11})\) | \(\Q(\sqrt{-11}) \) | \(0\) | \(0\) | \(-6\) | \(0\) | \(q+\beta _{1}q^{3}+(-2+\beta _{3})q^{5}+(-1+\beta _{3})q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(176, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(176, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 3}\)