Defining parameters
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(420\) | ||
Trace bound: | \(19\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(300, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 378 | 36 | 342 |
Cusp forms | 342 | 36 | 306 |
Eisenstein series | 36 | 0 | 36 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(300, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
300.7.b.a | $2$ | $69.016$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+3^{3}iq^{3}+683iq^{7}-3^{6}q^{9}-3527iq^{13}+\cdots\) |
300.7.b.b | $2$ | $69.016$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-3^{3}iq^{3}+397iq^{7}-3^{6}q^{9}-4033iq^{13}+\cdots\) |
300.7.b.c | $4$ | $69.016$ | \(\Q(i, \sqrt{5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-2\beta _{1}-\beta _{2})q^{3}-11^{2}\beta _{1}q^{7}+(711+\cdots)q^{9}+\cdots\) |
300.7.b.d | $12$ | $69.016$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-2\beta _{2}-\beta _{3})q^{3}+(12\beta _{2}+\beta _{3}-\beta _{11})q^{7}+\cdots\) |
300.7.b.e | $16$ | $69.016$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{3}q^{3}+(\beta _{4}-\beta _{5})q^{7}+(-187+\beta _{8}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{7}^{\mathrm{old}}(300, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(300, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)