Defining parameters
Level: | \( N \) | \(=\) | \( 275 = 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 275.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(60\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(275, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 36 | 16 | 20 |
Cusp forms | 24 | 16 | 8 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(275, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
275.2.b.a | $2$ | $2.196$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2 i q^{2}-i q^{3}-2 q^{4}+2 q^{6}+2 i q^{7}+\cdots\) |
275.2.b.b | $2$ | $2.196$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+i q^{2}+q^{4}+3 i q^{8}+3 q^{9}-q^{11}+\cdots\) |
275.2.b.c | $4$ | $2.196$ | \(\Q(i, \sqrt{13})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-2+\beta _{3})q^{4}+\cdots\) |
275.2.b.d | $4$ | $2.196$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta_1 q^{2}+(-\beta_{2}+\beta_1)q^{3}+(-\beta_{3}-1)q^{4}+\cdots\) |
275.2.b.e | $4$ | $2.196$ | \(\Q(i, \sqrt{5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(275, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(275, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)