Defining parameters
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.bb (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 65 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(420\) | ||
Trace bound: | \(19\) | ||
Distinguishing \(T_p\): | \(3\), \(7\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1300, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 456 | 44 | 412 |
Cusp forms | 384 | 44 | 340 |
Eisenstein series | 72 | 0 | 72 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1300, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(1300, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)