Defining parameters
Level: | \( N \) | \(=\) | \( 408 = 2^{3} \cdot 3 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 408.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(408))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 80 | 8 | 72 |
Cusp forms | 65 | 8 | 57 |
Eisenstein series | 15 | 0 | 15 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(17\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(2\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(1\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(1\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(1\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(3\) |
Plus space | \(+\) | \(3\) | ||
Minus space | \(-\) | \(5\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(408))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | 17 | |||||||
408.2.a.a | $1$ | $3.258$ | \(\Q\) | None | \(0\) | \(-1\) | \(3\) | \(0\) | $-$ | $+$ | $+$ | \(q-q^{3}+3q^{5}+q^{9}-q^{11}+3q^{13}+\cdots\) | |
408.2.a.b | $1$ | $3.258$ | \(\Q\) | None | \(0\) | \(1\) | \(-3\) | \(-4\) | $+$ | $-$ | $-$ | \(q+q^{3}-3q^{5}-4q^{7}+q^{9}+q^{11}-5q^{13}+\cdots\) | |
408.2.a.c | $1$ | $3.258$ | \(\Q\) | None | \(0\) | \(1\) | \(0\) | \(2\) | $+$ | $-$ | $+$ | \(q+q^{3}+2q^{7}+q^{9}+2q^{13}-q^{17}+\cdots\) | |
408.2.a.d | $1$ | $3.258$ | \(\Q\) | None | \(0\) | \(1\) | \(2\) | \(-4\) | $-$ | $-$ | $-$ | \(q+q^{3}+2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\) | |
408.2.a.e | $2$ | $3.258$ | \(\Q(\sqrt{17}) \) | None | \(0\) | \(-2\) | \(-1\) | \(-2\) | $+$ | $+$ | $+$ | \(q-q^{3}-\beta q^{5}+(-2+2\beta )q^{7}+q^{9}+\cdots\) | |
408.2.a.f | $2$ | $3.258$ | \(\Q(\sqrt{57}) \) | None | \(0\) | \(2\) | \(-1\) | \(8\) | $-$ | $-$ | $-$ | \(q+q^{3}-\beta q^{5}+4q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(408))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(408)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 2}\)