Defining parameters
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(300))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 78 | 4 | 74 |
Cusp forms | 43 | 4 | 39 |
Eisenstein series | 35 | 0 | 35 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(5\) | Fricke | Dim |
---|---|---|---|---|
\(-\) | \(+\) | \(+\) | \(-\) | \(1\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(1\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(2\) |
Plus space | \(+\) | \(1\) | ||
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(300))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | 5 | |||||||
300.2.a.a | $1$ | $2.396$ | \(\Q\) | None | \(0\) | \(-1\) | \(0\) | \(-4\) | $-$ | $+$ | $-$ | \(q-q^{3}-4q^{7}+q^{9}-4q^{11}-4q^{17}+\cdots\) | |
300.2.a.b | $1$ | $2.396$ | \(\Q\) | None | \(0\) | \(-1\) | \(0\) | \(1\) | $-$ | $+$ | $+$ | \(q-q^{3}+q^{7}+q^{9}+6q^{11}-5q^{13}+\cdots\) | |
300.2.a.c | $1$ | $2.396$ | \(\Q\) | None | \(0\) | \(1\) | \(0\) | \(-1\) | $-$ | $-$ | $-$ | \(q+q^{3}-q^{7}+q^{9}+6q^{11}+5q^{13}+\cdots\) | |
300.2.a.d | $1$ | $2.396$ | \(\Q\) | None | \(0\) | \(1\) | \(0\) | \(4\) | $-$ | $-$ | $-$ | \(q+q^{3}+4q^{7}+q^{9}-4q^{11}+4q^{17}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(300))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(300)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 2}\)