Defining parameters
Level: | \( N \) | \(=\) | \( 176 = 2^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 176.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 11 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(264\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{11}(176, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 246 | 61 | 185 |
Cusp forms | 234 | 59 | 175 |
Eisenstein series | 12 | 2 | 10 |
Trace form
Decomposition of \(S_{11}^{\mathrm{new}}(176, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
176.11.h.a | $1$ | $111.823$ | \(\Q\) | \(\Q(\sqrt{-11}) \) | \(0\) | \(-475\) | \(-3001\) | \(0\) | \(q-475q^{3}-3001q^{5}+166576q^{9}+\cdots\) |
176.11.h.b | $2$ | $111.823$ | \(\Q(\sqrt{33}) \) | \(\Q(\sqrt{-11}) \) | \(0\) | \(475\) | \(3001\) | \(0\) | \(q+(253-31\beta )q^{3}+(2327-1653\beta )q^{5}+\cdots\) |
176.11.h.c | $8$ | $111.823$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(-462\) | \(-3570\) | \(0\) | \(q+(-58-\beta _{1})q^{3}+(-446+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\) |
176.11.h.d | $8$ | $111.823$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(0\) | \(402\) | \(2430\) | \(0\) | \(q+(50-\beta _{5})q^{3}+(304+\beta _{5}+\beta _{6})q^{5}+\cdots\) |
176.11.h.e | $10$ | $111.823$ | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) | None | \(0\) | \(106\) | \(1138\) | \(0\) | \(q+(11+\beta _{1})q^{3}+(113-2\beta _{1}-\beta _{6})q^{5}+\cdots\) |
176.11.h.f | $30$ | $111.823$ | None | \(0\) | \(-44\) | \(0\) | \(0\) |
Decomposition of \(S_{11}^{\mathrm{old}}(176, [\chi])\) into lower level spaces
\( S_{11}^{\mathrm{old}}(176, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)