Defining parameters
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.h (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 25 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(40\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(175, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 88 | 64 | 24 |
Cusp forms | 72 | 64 | 8 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(175, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
175.2.h.a | $4$ | $1.397$ | \(\Q(\zeta_{10})\) | None | \(-5\) | \(-4\) | \(-5\) | \(-4\) | \(q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\) |
175.2.h.b | $28$ | $1.397$ | None | \(6\) | \(4\) | \(8\) | \(-28\) | ||
175.2.h.c | $32$ | $1.397$ | None | \(-3\) | \(-4\) | \(1\) | \(32\) |
Decomposition of \(S_{2}^{\mathrm{old}}(175, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(175, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)