Defining parameters
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.l (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 95 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(600\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1900, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 636 | 60 | 576 |
Cusp forms | 564 | 60 | 504 |
Eisenstein series | 72 | 0 | 72 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1900.2.l.a | $8$ | $15.172$ | 8.0.2702336256.1 | \(\Q(\sqrt{-19}) \) | \(0\) | \(0\) | \(0\) | \(6\) | \(q+(1+\beta _{1}+\beta _{5})q^{7}-3\beta _{1}q^{9}+(-1+\cdots)q^{11}+\cdots\) |
1900.2.l.b | $12$ | $15.172$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q-\beta _{2}q^{3}-\beta _{6}q^{7}+(\beta _{3}+4\beta _{5}-\beta _{6}+\cdots)q^{9}+\cdots\) |
1900.2.l.c | $16$ | $15.172$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{4}q^{3}+\beta _{9}q^{7}+(-\beta _{2}-\beta _{11})q^{9}+\cdots\) |
1900.2.l.d | $24$ | $15.172$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)