Defining parameters
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.i (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(100\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(175, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 172 | 108 | 64 |
Cusp forms | 148 | 96 | 52 |
Eisenstein series | 24 | 12 | 12 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(175, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
175.5.i.a | $4$ | $18.090$ | \(\Q(\sqrt{-3}, \sqrt{22})\) | None | \(4\) | \(-6\) | \(0\) | \(0\) | \(q+(2+\beta _{1}+2\beta _{2})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\) |
175.5.i.b | $20$ | $18.090$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(-6\) | \(18\) | \(0\) | \(54\) | \(q+(-1-\beta _{1}+\beta _{2}-\beta _{3})q^{2}+(1+\beta _{3}+\cdots)q^{3}+\cdots\) |
175.5.i.c | $22$ | $18.090$ | None | \(-3\) | \(9\) | \(0\) | \(82\) | ||
175.5.i.d | $22$ | $18.090$ | None | \(3\) | \(-9\) | \(0\) | \(-82\) | ||
175.5.i.e | $28$ | $18.090$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{5}^{\mathrm{old}}(175, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(175, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)