Defining parameters
Level: | \( N \) | \(=\) | \( 190 = 2 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 190.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(60\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(190, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 34 | 10 | 24 |
Cusp forms | 26 | 10 | 16 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(190, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
190.2.b.a | $4$ | $1.517$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{8}^{2}q^{2}+(\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-q^{4}+\cdots\) |
190.2.b.b | $6$ | $1.517$ | 6.0.5161984.1 | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q-\beta _{4}q^{2}+(\beta _{4}+\beta _{5})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(190, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(190, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)