Defining parameters
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.ba (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 65 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(420\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1300, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 456 | 40 | 416 |
Cusp forms | 384 | 40 | 344 |
Eisenstein series | 72 | 0 | 72 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1300, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1300.2.ba.a | $4$ | $10.381$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}q^{3}+(\zeta_{12}+\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{9}+\cdots\) |
1300.2.ba.b | $8$ | $10.381$ | 8.0.22581504.2 | None | \(0\) | \(-6\) | \(0\) | \(6\) | \(q+(\beta _{2}+\beta _{6})q^{3}+(1-\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\) |
1300.2.ba.c | $8$ | $10.381$ | 8.0.22581504.2 | None | \(0\) | \(6\) | \(0\) | \(-6\) | \(q+(-\beta _{2}-\beta _{6})q^{3}+(-1+\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\) |
1300.2.ba.d | $20$ | $10.381$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{18}q^{3}+(-\beta _{10}-\beta _{16}-\beta _{19})q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1300, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)