Defining parameters
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 65 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(420\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(3\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1300, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 228 | 20 | 208 |
Cusp forms | 192 | 20 | 172 |
Eisenstein series | 36 | 0 | 36 |
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.d.a | $4$ | $10.381$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-2\zeta_{12}q^{3}-\zeta_{12}^{3}q^{7}-q^{9}+3\zeta_{12}^{2}q^{11}+\cdots\) |
1300.2.d.b | $4$ | $10.381$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}q^{3}+\zeta_{12}^{3}q^{7}+2q^{9}+(\zeta_{12}+\cdots)q^{13}+\cdots\) |
1300.2.d.c | $6$ | $10.381$ | 6.0.9144576.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}+\beta _{3}q^{7}+(-1+\beta _{3})q^{9}+(\beta _{4}+\cdots)q^{11}+\cdots\) |
1300.2.d.d | $6$ | $10.381$ | 6.0.9144576.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}-\beta _{3}q^{7}+(-1+\beta _{3})q^{9}+(-\beta _{4}+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1300, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)