Defining parameters
Level: | \( N \) | \(=\) | \( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1476.bb (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 41 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(504\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1476, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1056 | 72 | 984 |
Cusp forms | 960 | 72 | 888 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1476, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1476.2.bb.a | $8$ | $11.786$ | 8.0.26265625.1 | None | \(0\) | \(0\) | \(0\) | \(20\) | \(q+(-\beta _{2}-\beta _{7})q^{5}+(2+2\beta _{1})q^{7}+(2\beta _{2}+\cdots)q^{11}+\cdots\) |
1476.2.bb.b | $16$ | $11.786$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(-4\) | \(0\) | \(q+\beta _{12}q^{5}+(-\beta _{9}+\beta _{14})q^{7}+(\beta _{3}+\beta _{5}+\cdots)q^{11}+\cdots\) |
1476.2.bb.c | $24$ | $11.786$ | None | \(0\) | \(0\) | \(0\) | \(-20\) | ||
1476.2.bb.d | $24$ | $11.786$ | None | \(0\) | \(0\) | \(4\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1476, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1476, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(123, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(246, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(369, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(492, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(738, [\chi])\)\(^{\oplus 2}\)