Defining parameters
Level: | \( N \) | \(=\) | \( 138 = 2 \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 138.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(138))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 76 | 10 | 66 |
Cusp forms | 68 | 10 | 58 |
Eisenstein series | 8 | 0 | 8 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(23\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(-\) | $-$ | \(1\) |
\(+\) | \(-\) | \(+\) | $-$ | \(1\) |
\(+\) | \(-\) | \(-\) | $+$ | \(2\) |
\(-\) | \(+\) | \(+\) | $-$ | \(1\) |
\(-\) | \(+\) | \(-\) | $+$ | \(2\) |
\(-\) | \(-\) | \(+\) | $+$ | \(3\) |
Plus space | \(+\) | \(7\) | ||
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(138))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | 23 | |||||||
138.4.a.a | $1$ | $8.142$ | \(\Q\) | None | \(-2\) | \(-3\) | \(-10\) | \(32\) | $+$ | $+$ | $-$ | \(q-2q^{2}-3q^{3}+4q^{4}-10q^{5}+6q^{6}+\cdots\) | |
138.4.a.b | $1$ | $8.142$ | \(\Q\) | None | \(-2\) | \(3\) | \(2\) | \(-32\) | $+$ | $-$ | $+$ | \(q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots\) | |
138.4.a.c | $1$ | $8.142$ | \(\Q\) | None | \(2\) | \(-3\) | \(-2\) | \(-34\) | $-$ | $+$ | $+$ | \(q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots\) | |
138.4.a.d | $2$ | $8.142$ | \(\Q(\sqrt{277}) \) | None | \(-4\) | \(6\) | \(2\) | \(28\) | $+$ | $-$ | $-$ | \(q-2q^{2}+3q^{3}+4q^{4}+(1-\beta )q^{5}-6q^{6}+\cdots\) | |
138.4.a.e | $2$ | $8.142$ | \(\Q(\sqrt{2}) \) | None | \(4\) | \(-6\) | \(8\) | \(12\) | $-$ | $+$ | $-$ | \(q+2q^{2}-3q^{3}+4q^{4}+(4+\beta )q^{5}-6q^{6}+\cdots\) | |
138.4.a.f | $3$ | $8.142$ | 3.3.16372.1 | None | \(6\) | \(9\) | \(20\) | \(10\) | $-$ | $-$ | $+$ | \(q+2q^{2}+3q^{3}+4q^{4}+(7+\beta _{2})q^{5}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(138))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(138)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 2}\)