Defining parameters
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(28\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(143))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 16 | 11 | 5 |
Cusp forms | 13 | 11 | 2 |
Eisenstein series | 3 | 0 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(11\) | \(13\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(-\) | $-$ | \(6\) |
\(-\) | \(+\) | $-$ | \(4\) |
Plus space | \(+\) | \(1\) | |
Minus space | \(-\) | \(10\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(143))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 11 | 13 | |||||||
143.2.a.a | $1$ | $1.142$ | \(\Q\) | None | \(0\) | \(-1\) | \(-1\) | \(-2\) | $+$ | $+$ | \(q-q^{3}-2q^{4}-q^{5}-2q^{7}-2q^{9}-q^{11}+\cdots\) | |
143.2.a.b | $4$ | $1.142$ | 4.4.1957.1 | None | \(3\) | \(0\) | \(0\) | \(6\) | $-$ | $+$ | \(q+(1+\beta _{1}+\beta _{2})q^{2}+(-\beta _{2}-\beta _{3})q^{3}+\cdots\) | |
143.2.a.c | $6$ | $1.142$ | 6.6.194616205.1 | None | \(0\) | \(3\) | \(1\) | \(4\) | $+$ | $-$ | \(q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(143))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(143)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)