Defining parameters
Level: | \( N \) | \(=\) | \( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2300.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 15 \) | ||
Sturm bound: | \(720\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2300))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 378 | 36 | 342 |
Cusp forms | 343 | 36 | 307 |
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.
\(2\) | \(5\) | \(23\) | Fricke | Dim |
---|---|---|---|---|
\(-\) | \(+\) | \(+\) | $-$ | \(8\) |
\(-\) | \(+\) | \(-\) | $+$ | \(8\) |
\(-\) | \(-\) | \(+\) | $+$ | \(10\) |
\(-\) | \(-\) | \(-\) | $-$ | \(10\) |
Plus space | \(+\) | \(18\) | ||
Minus space | \(-\) | \(18\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2300))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2300))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(2300)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(575))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1150))\)\(^{\oplus 2}\)