Defining parameters
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\), \(3\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(245, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 36 | 26 | 10 |
Cusp forms | 20 | 16 | 4 |
Eisenstein series | 16 | 10 | 6 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(245, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
245.2.b.a | $2$ | $1.956$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q+2iq^{2}+iq^{3}-2q^{4}+(2+i)q^{5}+\cdots\) |
245.2.b.b | $2$ | $1.956$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+iq^{2}-iq^{3}+q^{4}+(-1+2i)q^{5}+\cdots\) |
245.2.b.c | $2$ | $1.956$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+iq^{2}+iq^{3}+q^{4}+(1-2i)q^{5}-q^{6}+\cdots\) |
245.2.b.d | $2$ | $1.956$ | \(\Q(\sqrt{-5}) \) | \(\Q(\sqrt{-35}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta q^{3}+2q^{4}+\beta q^{5}-2q^{9}-3q^{11}+\cdots\) |
245.2.b.e | $4$ | $1.956$ | \(\Q(\sqrt{2}, \sqrt{-3})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{3}q^{2}+\beta _{2}q^{3}-4q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\) |
245.2.b.f | $4$ | $1.956$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{8}^{2}q^{2}+(2\zeta_{8}+2\zeta_{8}^{3})q^{3}+q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(245, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(245, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)