Defining parameters
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.h (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 25 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(350, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 256 | 56 | 200 |
Cusp forms | 224 | 56 | 168 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(350, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
350.2.h.a | $8$ | $2.795$ | \(\Q(\zeta_{15})\) | None | \(-2\) | \(3\) | \(0\) | \(8\) | \(q+\zeta_{15}^{4}q^{2}+(-\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{6}+\cdots)q^{3}+\cdots\) |
350.2.h.b | $12$ | $2.795$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(3\) | \(1\) | \(-5\) | \(-12\) | \(q+\beta _{5}q^{2}+(\beta _{1}-\beta _{3}+\beta _{7})q^{3}-\beta _{3}q^{4}+\cdots\) |
350.2.h.c | $16$ | $2.795$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(-4\) | \(1\) | \(-4\) | \(-16\) | \(q+\beta _{6}q^{2}-\beta _{10}q^{3}-\beta _{1}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\) |
350.2.h.d | $20$ | $2.795$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(5\) | \(3\) | \(-5\) | \(20\) | \(q+\beta _{14}q^{2}+\beta _{1}q^{3}+\beta _{6}q^{4}+(\beta _{10}+\beta _{13}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(350, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(350, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)