Defining parameters
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(11\), \(17\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(210))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 56 | 5 | 51 |
Cusp forms | 41 | 5 | 36 |
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.
\(2\) | \(3\) | \(5\) | \(7\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(1\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(1\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(1\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(1\) |
Plus space | \(+\) | \(1\) | |||
Minus space | \(-\) | \(4\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(210))\) 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 | 7 | |||||||
210.2.a.a | $1$ | $1.677$ | \(\Q\) | None | \(-1\) | \(-1\) | \(-1\) | \(-1\) | $+$ | $+$ | $+$ | $+$ | \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\) | |
210.2.a.b | $1$ | $1.677$ | \(\Q\) | None | \(-1\) | \(1\) | \(1\) | \(1\) | $+$ | $-$ | $-$ | $-$ | \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\) | |
210.2.a.c | $1$ | $1.677$ | \(\Q\) | None | \(1\) | \(-1\) | \(1\) | \(1\) | $-$ | $+$ | $-$ | $-$ | \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\) | |
210.2.a.d | $1$ | $1.677$ | \(\Q\) | None | \(1\) | \(1\) | \(-1\) | \(1\) | $-$ | $-$ | $+$ | $-$ | \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\) | |
210.2.a.e | $1$ | $1.677$ | \(\Q\) | None | \(1\) | \(1\) | \(1\) | \(-1\) | $-$ | $-$ | $-$ | $+$ | \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(210))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(210)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 2}\)