Defining parameters
Level: | \( N \) | \(=\) | \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3380.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 19 \) | ||
Sturm bound: | \(1092\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\), \(7\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3380))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 588 | 51 | 537 |
Cusp forms | 505 | 51 | 454 |
Eisenstein series | 83 | 0 | 83 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(5\) | \(13\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | |||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(70\) | \(0\) | \(70\) | \(57\) | \(0\) | \(57\) | \(13\) | \(0\) | \(13\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(80\) | \(0\) | \(80\) | \(66\) | \(0\) | \(66\) | \(14\) | \(0\) | \(14\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(77\) | \(0\) | \(77\) | \(63\) | \(0\) | \(63\) | \(14\) | \(0\) | \(14\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(73\) | \(0\) | \(73\) | \(59\) | \(0\) | \(59\) | \(14\) | \(0\) | \(14\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(77\) | \(16\) | \(61\) | \(70\) | \(16\) | \(54\) | \(7\) | \(0\) | \(7\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(67\) | \(10\) | \(57\) | \(60\) | \(10\) | \(50\) | \(7\) | \(0\) | \(7\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(70\) | \(9\) | \(61\) | \(63\) | \(9\) | \(54\) | \(7\) | \(0\) | \(7\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(74\) | \(16\) | \(58\) | \(67\) | \(16\) | \(51\) | \(7\) | \(0\) | \(7\) | |||
Plus space | \(+\) | \(280\) | \(19\) | \(261\) | \(239\) | \(19\) | \(220\) | \(41\) | \(0\) | \(41\) | |||||
Minus space | \(-\) | \(308\) | \(32\) | \(276\) | \(266\) | \(32\) | \(234\) | \(42\) | \(0\) | \(42\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3380))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3380))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(3380)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(676))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(845))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1690))\)\(^{\oplus 2}\)