Defining parameters
Level: | \( N \) | \(=\) | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 276.i (of order \(11\) and degree \(10\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 23 \) |
Character field: | \(\Q(\zeta_{11})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(276, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 540 | 40 | 500 |
Cusp forms | 420 | 40 | 380 |
Eisenstein series | 120 | 0 | 120 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(276, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
276.2.i.a | $20$ | $2.204$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(-2\) | \(-4\) | \(0\) | \(q+\beta _{17}q^{3}+(\beta _{3}+\beta _{4}-\beta _{9}-\beta _{10}+\beta _{15}+\cdots)q^{5}+\cdots\) |
276.2.i.b | $20$ | $2.204$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(2\) | \(0\) | \(-4\) | \(q-\beta _{5}q^{3}+(1-\beta _{3}+\beta _{5}+\beta _{7}+\beta _{10}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(276, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(276, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)