Defining parameters
Level: | \( N \) | \(=\) | \( 1596 = 2^{2} \cdot 3 \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1596.i (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 133 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(640\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1596, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 332 | 28 | 304 |
Cusp forms | 308 | 28 | 280 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1596, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1596.2.i.a | $14$ | $12.744$ | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) | None | \(0\) | \(-14\) | \(0\) | \(-1\) | \(q-q^{3}-\beta _{10}q^{5}+\beta _{11}q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\) |
1596.2.i.b | $14$ | $12.744$ | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) | None | \(0\) | \(14\) | \(0\) | \(-1\) | \(q+q^{3}-\beta _{10}q^{5}+\beta _{11}q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1596, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1596, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(532, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)