Defining parameters
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 19 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(76\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{19}(35, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 74 | 74 | 0 |
Cusp forms | 70 | 70 | 0 |
Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{19}^{\mathrm{new}}(35, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
35.19.c.a | $1$ | $71.885$ | \(\Q\) | \(\Q(\sqrt{-35}) \) | \(0\) | \(-39286\) | \(1953125\) | \(-40353607\) | \(q-39286q^{3}+2^{18}q^{4}+5^{9}q^{5}-7^{9}q^{7}+\cdots\) |
35.19.c.b | $1$ | $71.885$ | \(\Q\) | \(\Q(\sqrt{-35}) \) | \(0\) | \(39286\) | \(-1953125\) | \(40353607\) | \(q+39286q^{3}+2^{18}q^{4}-5^{9}q^{5}+7^{9}q^{7}+\cdots\) |
35.19.c.c | $68$ | $71.885$ | None | \(0\) | \(0\) | \(0\) | \(0\) |