Defining parameters
Level: | \( N \) | \(=\) | \( 312 = 2^{3} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 312.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(112\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(312))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 64 | 6 | 58 |
Cusp forms | 49 | 6 | 43 |
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.
\(2\) | \(3\) | \(13\) | Fricke | Dim. |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(1\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(1\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(1\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(1\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(1\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(1\) |
Plus space | \(+\) | \(2\) | ||
Minus space | \(-\) | \(4\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(312))\) into newform subspaces
Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 2 | 3 | 13 | |||||||
312.2.a.a | \(1\) | \(2.491\) | \(\Q\) | None | \(0\) | \(-1\) | \(-2\) | \(4\) | \(+\) | \(+\) | \(-\) | \(q-q^{3}-2q^{5}+4q^{7}+q^{9}+q^{13}+2q^{15}+\cdots\) | |
312.2.a.b | \(1\) | \(2.491\) | \(\Q\) | None | \(0\) | \(-1\) | \(0\) | \(-4\) | \(+\) | \(+\) | \(+\) | \(q-q^{3}-4q^{7}+q^{9}-2q^{11}-q^{13}+\cdots\) | |
312.2.a.c | \(1\) | \(2.491\) | \(\Q\) | None | \(0\) | \(-1\) | \(4\) | \(0\) | \(-\) | \(+\) | \(+\) | \(q-q^{3}+4q^{5}+q^{9}-2q^{11}-q^{13}+\cdots\) | |
312.2.a.d | \(1\) | \(2.491\) | \(\Q\) | None | \(0\) | \(1\) | \(-4\) | \(-4\) | \(-\) | \(-\) | \(+\) | \(q+q^{3}-4q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots\) | |
312.2.a.e | \(1\) | \(2.491\) | \(\Q\) | None | \(0\) | \(1\) | \(0\) | \(0\) | \(+\) | \(-\) | \(+\) | \(q+q^{3}+q^{9}+6q^{11}-q^{13}+2q^{17}+\cdots\) | |
312.2.a.f | \(1\) | \(2.491\) | \(\Q\) | None | \(0\) | \(1\) | \(2\) | \(0\) | \(-\) | \(-\) | \(-\) | \(q+q^{3}+2q^{5}+q^{9}+q^{13}+2q^{15}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(312))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(312)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 2}\)