Defining parameters
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(74\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(403))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 38 | 31 | 7 |
Cusp forms | 35 | 31 | 4 |
Eisenstein series | 3 | 0 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(13\) | \(31\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(8\) |
\(+\) | \(-\) | $-$ | \(7\) |
\(-\) | \(+\) | $-$ | \(10\) |
\(-\) | \(-\) | $+$ | \(6\) |
Plus space | \(+\) | \(14\) | |
Minus space | \(-\) | \(17\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(403))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 13 | 31 | |||||||
403.2.a.a | $2$ | $3.218$ | \(\Q(\sqrt{5}) \) | None | \(3\) | \(-4\) | \(0\) | \(2\) | $-$ | $+$ | \(q+(1+\beta )q^{2}-2q^{3}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots\) | |
403.2.a.b | $6$ | $3.218$ | 6.6.5748973.1 | None | \(-2\) | \(-5\) | \(-9\) | \(0\) | $-$ | $-$ | \(q+\beta _{4}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\) | |
403.2.a.c | $7$ | $3.218$ | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) | None | \(2\) | \(5\) | \(11\) | \(4\) | $+$ | $-$ | \(q+\beta _{3}q^{2}+(1-\beta _{1})q^{3}+(\beta _{1}+\beta _{4}+\beta _{6})q^{4}+\cdots\) | |
403.2.a.d | $8$ | $3.218$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(-5\) | \(-3\) | \(-15\) | \(-4\) | $+$ | $+$ | \(q+(-1+\beta _{1})q^{2}-\beta _{6}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\) | |
403.2.a.e | $8$ | $3.218$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(-1\) | \(7\) | \(11\) | \(-2\) | $-$ | $+$ | \(q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(403))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(403)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 2}\)