Defining parameters
Level: | \( N \) | \(=\) | \( 476 = 2^{2} \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 476.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(476))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 78 | 8 | 70 |
Cusp forms | 67 | 8 | 59 |
Eisenstein series | 11 | 0 | 11 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(7\) | \(17\) | Fricke | Dim |
---|---|---|---|---|
\(-\) | \(+\) | \(+\) | \(-\) | \(2\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(2\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(2\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(2\) |
Plus space | \(+\) | \(4\) | ||
Minus space | \(-\) | \(4\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(476))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 7 | 17 | |||||||
476.2.a.a | $2$ | $3.801$ | \(\Q(\sqrt{13}) \) | None | \(0\) | \(-3\) | \(-3\) | \(2\) | $-$ | $-$ | $+$ | \(q+(-1-\beta )q^{3}+(-2+\beta )q^{5}+q^{7}+\cdots\) | |
476.2.a.b | $2$ | $3.801$ | \(\Q(\sqrt{5}) \) | None | \(0\) | \(-1\) | \(-1\) | \(-2\) | $-$ | $+$ | $-$ | \(q-\beta q^{3}+(-1+\beta )q^{5}-q^{7}+(-2+\beta )q^{9}+\cdots\) | |
476.2.a.c | $2$ | $3.801$ | \(\Q(\sqrt{13}) \) | None | \(0\) | \(-1\) | \(1\) | \(-2\) | $-$ | $+$ | $+$ | \(q-\beta q^{3}+(1-\beta )q^{5}-q^{7}+\beta q^{9}+4q^{11}+\cdots\) | |
476.2.a.d | $2$ | $3.801$ | \(\Q(\sqrt{13}) \) | None | \(0\) | \(1\) | \(-1\) | \(2\) | $-$ | $-$ | $-$ | \(q+\beta q^{3}+(-1+\beta )q^{5}+q^{7}+\beta q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(476))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(476)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 2}\)