Defining parameters
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(380))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 66 | 6 | 60 |
Cusp forms | 55 | 6 | 49 |
Eisenstein series | 11 | 0 | 11 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(5\) | \(19\) | Fricke | Dim |
---|---|---|---|---|
\(-\) | \(+\) | \(+\) | \(-\) | \(1\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(1\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(2\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(2\) |
Plus space | \(+\) | \(3\) | ||
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(380))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 5 | 19 | |||||||
380.2.a.a | $1$ | $3.034$ | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(-2\) | $-$ | $+$ | $-$ | \(q-q^{5}-2q^{7}-3q^{9}-4q^{11}-4q^{13}+\cdots\) | |
380.2.a.b | $1$ | $3.034$ | \(\Q\) | None | \(0\) | \(2\) | \(-1\) | \(2\) | $-$ | $+$ | $+$ | \(q+2q^{3}-q^{5}+2q^{7}+q^{9}+6q^{13}+\cdots\) | |
380.2.a.c | $2$ | $3.034$ | \(\Q(\sqrt{2}) \) | None | \(0\) | \(-4\) | \(2\) | \(-4\) | $-$ | $-$ | $+$ | \(q+(-2+\beta )q^{3}+q^{5}+(-2-2\beta )q^{7}+\cdots\) | |
380.2.a.d | $2$ | $3.034$ | \(\Q(\sqrt{3}) \) | None | \(0\) | \(2\) | \(2\) | \(4\) | $-$ | $-$ | $-$ | \(q+(1+\beta )q^{3}+q^{5}+2q^{7}+(1+2\beta )q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(380))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(380)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 2}\)