Defining parameters
Level: | \( N \) | \(=\) | \( 176 = 2^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
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: | \(216\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(176, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 198 | 49 | 149 |
Cusp forms | 186 | 47 | 139 |
Eisenstein series | 12 | 2 | 10 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(176, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
176.9.h.a | $1$ | $71.699$ | \(\Q\) | \(\Q(\sqrt{-11}) \) | \(0\) | \(113\) | \(1151\) | \(0\) | \(q+113q^{3}+1151q^{5}+6208q^{9}-11^{4}q^{11}+\cdots\) |
176.9.h.b | $2$ | $71.699$ | \(\Q(\sqrt{33}) \) | \(\Q(\sqrt{-11}) \) | \(0\) | \(-113\) | \(-1151\) | \(0\) | \(q+(-59-5\beta )q^{3}+(-565+21\beta )q^{5}+\cdots\) |
176.9.h.c | $6$ | $71.699$ | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) | None | \(0\) | \(36\) | \(-448\) | \(0\) | \(q+(6+\beta _{5})q^{3}+(-73-5\beta _{4}-3\beta _{5})q^{5}+\cdots\) |
176.9.h.d | $6$ | $71.699$ | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) | None | \(0\) | \(36\) | \(1856\) | \(0\) | \(q+(6+\beta _{2})q^{3}+(309+\beta _{5})q^{5}+\beta _{1}q^{7}+\cdots\) |
176.9.h.e | $8$ | $71.699$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(0\) | \(-182\) | \(-1410\) | \(0\) | \(q+(-23-\beta _{1})q^{3}+(-176+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\) |
176.9.h.f | $24$ | $71.699$ | None | \(0\) | \(112\) | \(0\) | \(0\) |
Decomposition of \(S_{9}^{\mathrm{old}}(176, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(176, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)