Defining parameters
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.g (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(30\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(45, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 56 | 22 | 34 |
Cusp forms | 40 | 18 | 22 |
Eisenstein series | 16 | 4 | 12 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(45, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
45.5.g.a | $2$ | $4.652$ | \(\Q(\sqrt{-1}) \) | None | \(-10\) | \(0\) | \(50\) | \(80\) | \(q+(-5 i-5)q^{2}+34 i q^{4}+25 q^{5}+\cdots\) |
45.5.g.b | $2$ | $4.652$ | \(\Q(\sqrt{-1}) \) | None | \(2\) | \(0\) | \(-40\) | \(-52\) | \(q+(i+1)q^{2}-14 i q^{4}+(-15 i-20)q^{5}+\cdots\) |
45.5.g.c | $2$ | $4.652$ | \(\Q(\sqrt{-1}) \) | None | \(10\) | \(0\) | \(-50\) | \(80\) | \(q+(5 i+5)q^{2}+34 i q^{4}-25 q^{5}+\cdots\) |
45.5.g.d | $4$ | $4.652$ | \(\Q(i, \sqrt{10})\) | None | \(0\) | \(0\) | \(0\) | \(-20\) | \(q+\beta _{1}q^{2}-11\beta _{2}q^{4}+(2\beta _{1}-11\beta _{3})q^{5}+\cdots\) |
45.5.g.e | $8$ | $4.652$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(0\) | \(84\) | \(20\) | \(q+\beta _{3}q^{2}+(\beta _{1}-12\beta _{2}+\beta _{3}+\beta _{5})q^{4}+\cdots\) |
Decomposition of \(S_{5}^{\mathrm{old}}(45, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)