Defining parameters
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.k (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(80\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(175, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 132 | 76 | 56 |
Cusp forms | 108 | 68 | 40 |
Eisenstein series | 24 | 8 | 16 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(175, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
175.4.k.a | $4$ | $10.325$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2\zeta_{12}q^{2}+(7\zeta_{12}-7\zeta_{12}^{3})q^{3}-4\zeta_{12}^{2}q^{4}+\cdots\) |
175.4.k.b | $4$ | $10.325$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+3\zeta_{12}q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\) |
175.4.k.c | $8$ | $10.325$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{24}^{3}+2\zeta_{24}^{7})q^{2}+(-2\zeta_{24}^{2}+\cdots)q^{3}+\cdots\) |
175.4.k.d | $20$ | $10.325$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{1}-\beta _{14})q^{2}+(\beta _{6}+\beta _{8})q^{3}+(7-7\beta _{7}+\cdots)q^{4}+\cdots\) |
175.4.k.e | $32$ | $10.325$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{4}^{\mathrm{old}}(175, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(175, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)