Defining parameters
Level: | \( N \) | \(=\) | \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1260.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(10\) | ||
Distinguishing \(T_p\): | \(11\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1260, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 304 | 80 | 224 |
Cusp forms | 272 | 80 | 192 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1260, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1260.2.c.a | $4$ | $10.061$ | \(\Q(\zeta_{12})\) | None | \(2\) | \(0\) | \(0\) | \(0\) | \(q+(\beta_{3}+1)q^{2}+(\beta_{3}-2\beta_{2}+\beta_1)q^{4}+\cdots\) |
1260.2.c.b | $4$ | $10.061$ | \(\Q(\zeta_{12})\) | None | \(2\) | \(0\) | \(0\) | \(0\) | \(q+(\beta_{3}+1)q^{2}+(\beta_{3}-2\beta_{2}+\beta_1)q^{4}+\cdots\) |
1260.2.c.c | $8$ | $10.061$ | 8.0.342102016.5 | None | \(-2\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{4}q^{2}+(-\beta _{3}-\beta _{4}-\beta _{5})q^{4}+\beta _{2}q^{5}+\cdots\) |
1260.2.c.d | $16$ | $10.061$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(-2\) | \(0\) | \(0\) | \(-4\) | \(q+\beta _{4}q^{2}+\beta _{8}q^{4}+\beta _{3}q^{5}+(-\beta _{9}-\beta _{10}+\cdots)q^{7}+\cdots\) |
1260.2.c.e | $16$ | $10.061$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(-2\) | \(0\) | \(0\) | \(4\) | \(q+\beta _{4}q^{2}+\beta _{8}q^{4}-\beta _{3}q^{5}-\beta _{15}q^{7}+\cdots\) |
1260.2.c.f | $32$ | $10.061$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1260, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1260, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)