Defining parameters
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(3\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(700))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 138 | 10 | 128 |
Cusp forms | 103 | 10 | 93 |
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.
\(2\) | \(5\) | \(7\) | Fricke | Dim. |
---|---|---|---|---|
\(-\) | \(+\) | \(+\) | \(-\) | \(2\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(2\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(3\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(3\) |
Plus space | \(+\) | \(5\) | ||
Minus space | \(-\) | \(5\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(700))\) into newform subspaces
Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 2 | 5 | 7 | |||||||
700.2.a.a | \(1\) | \(5.590\) | \(\Q\) | None | \(0\) | \(-3\) | \(0\) | \(-1\) | \(-\) | \(-\) | \(+\) | \(q-3q^{3}-q^{7}+6q^{9}+3q^{11}-q^{13}+\cdots\) | |
700.2.a.b | \(1\) | \(5.590\) | \(\Q\) | None | \(0\) | \(-3\) | \(0\) | \(1\) | \(-\) | \(+\) | \(-\) | \(q-3q^{3}+q^{7}+6q^{9}-5q^{11}+3q^{13}+\cdots\) | |
700.2.a.c | \(1\) | \(5.590\) | \(\Q\) | None | \(0\) | \(-2\) | \(0\) | \(1\) | \(-\) | \(-\) | \(-\) | \(q-2q^{3}+q^{7}+q^{9}+3q^{11}-4q^{13}+\cdots\) | |
700.2.a.d | \(1\) | \(5.590\) | \(\Q\) | None | \(0\) | \(-1\) | \(0\) | \(-1\) | \(-\) | \(+\) | \(+\) | \(q-q^{3}-q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots\) | |
700.2.a.e | \(1\) | \(5.590\) | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(-1\) | \(-\) | \(-\) | \(+\) | \(q-q^{7}-3q^{9}-5q^{11}+6q^{13}-4q^{17}+\cdots\) | |
700.2.a.f | \(1\) | \(5.590\) | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(-1\) | \(-\) | \(-\) | \(+\) | \(q-q^{7}-3q^{9}-4q^{13}-4q^{17}+4q^{19}+\cdots\) | |
700.2.a.g | \(1\) | \(5.590\) | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(1\) | \(-\) | \(+\) | \(-\) | \(q+q^{7}-3q^{9}-5q^{11}-6q^{13}+4q^{17}+\cdots\) | |
700.2.a.h | \(1\) | \(5.590\) | \(\Q\) | None | \(0\) | \(0\) | \(0\) | \(1\) | \(-\) | \(-\) | \(-\) | \(q+q^{7}-3q^{9}+4q^{13}+4q^{17}+4q^{19}+\cdots\) | |
700.2.a.i | \(1\) | \(5.590\) | \(\Q\) | None | \(0\) | \(2\) | \(0\) | \(-1\) | \(-\) | \(+\) | \(+\) | \(q+2q^{3}-q^{7}+q^{9}+3q^{11}+4q^{13}+\cdots\) | |
700.2.a.j | \(1\) | \(5.590\) | \(\Q\) | None | \(0\) | \(3\) | \(0\) | \(1\) | \(-\) | \(-\) | \(-\) | \(q+3q^{3}+q^{7}+6q^{9}+3q^{11}+q^{13}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(700))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(700)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 2}\)