Defining parameters
Level: | \( N \) | \(=\) | \( 435 = 3 \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 435.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 145 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(435, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 64 | 32 | 32 |
Cusp forms | 56 | 32 | 24 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(435, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
435.2.f.a | $2$ | $3.473$ | \(\Q(\sqrt{-1}) \) | None | \(-4\) | \(2\) | \(4\) | \(0\) | \(q-2q^{2}+q^{3}+2q^{4}+(2+i)q^{5}-2q^{6}+\cdots\) |
435.2.f.b | $2$ | $3.473$ | \(\Q(\sqrt{-1}) \) | None | \(-2\) | \(-2\) | \(-2\) | \(0\) | \(q-q^{2}-q^{3}-q^{4}+(-1+i)q^{5}+q^{6}+\cdots\) |
435.2.f.c | $2$ | $3.473$ | \(\Q(\sqrt{-1}) \) | None | \(2\) | \(2\) | \(-2\) | \(0\) | \(q+q^{2}+q^{3}-q^{4}+(-1+i)q^{5}+q^{6}+\cdots\) |
435.2.f.d | $2$ | $3.473$ | \(\Q(\sqrt{-1}) \) | None | \(4\) | \(-2\) | \(4\) | \(0\) | \(q+2q^{2}-q^{3}+2q^{4}+(2+i)q^{5}-2q^{6}+\cdots\) |
435.2.f.e | $12$ | $3.473$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(-12\) | \(-6\) | \(0\) | \(q+\beta _{5}q^{2}-q^{3}+(1-\beta _{3})q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\) |
435.2.f.f | $12$ | $3.473$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(12\) | \(-6\) | \(0\) | \(q-\beta _{5}q^{2}+q^{3}+(1-\beta _{3})q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(435, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(435, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)