Defining parameters
Level: | \( N \) | \(=\) | \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1260.k (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1260, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 312 | 16 | 296 |
Cusp forms | 264 | 16 | 248 |
Eisenstein series | 48 | 0 | 48 |
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.k.a | $2$ | $10.061$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q+(-2-i)q^{5}-iq^{7}-4q^{11}+2iq^{13}+\cdots\) |
1260.2.k.b | $2$ | $10.061$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+(-1-2i)q^{5}+iq^{7}-4iq^{13}-4iq^{17}+\cdots\) |
1260.2.k.c | $2$ | $10.061$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q+(2+i)q^{5}+iq^{7}-3q^{11}-iq^{13}+\cdots\) |
1260.2.k.d | $2$ | $10.061$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(4\) | \(0\) | \(q+(2-i)q^{5}-iq^{7}+4q^{11}-6iq^{13}+\cdots\) |
1260.2.k.e | $8$ | $10.061$ | 8.0.49787136.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{7}q^{5}-\beta _{1}q^{7}+(\beta _{3}+\beta _{4}+\beta _{5}+\beta _{7})q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1260, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)