Defining parameters
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.g (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 95 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(100\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(475, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 112 | 64 | 48 |
Cusp forms | 88 | 56 | 32 |
Eisenstein series | 24 | 8 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(475, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
475.2.g.a | $4$ | $3.793$ | \(\Q(i, \sqrt{19})\) | \(\Q(\sqrt{-19}) \) | \(0\) | \(0\) | \(0\) | \(-6\) | \(q-2\beta _{1}q^{4}+(-2+2\beta _{1}+\beta _{3})q^{7}+3\beta _{1}q^{9}+\cdots\) |
475.2.g.b | $12$ | $3.793$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(12\) | \(q-\beta _{7}q^{2}+\beta _{5}q^{3}+(-\beta _{6}-\beta _{8})q^{4}+\cdots\) |
475.2.g.c | $16$ | $3.793$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | \(\Q(\sqrt{-95}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{9}q^{2}-\beta _{3}q^{3}+(-2\beta _{7}-\beta _{10})q^{4}+\cdots\) |
475.2.g.d | $24$ | $3.793$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(475, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(475, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)