Defining parameters
Level: | \( N \) | \(=\) | \( 740 = 2^{2} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 740.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(456\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(740))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 348 | 36 | 312 |
Cusp forms | 336 | 36 | 300 |
Eisenstein series | 12 | 0 | 12 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(5\) | \(37\) | Fricke | Dim |
---|---|---|---|---|
\(-\) | \(+\) | \(+\) | \(-\) | \(8\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(11\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(11\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(6\) |
Plus space | \(+\) | \(22\) | ||
Minus space | \(-\) | \(14\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(740))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 5 | 37 | |||||||
740.4.a.a | $1$ | $43.661$ | \(\Q\) | None | \(0\) | \(-8\) | \(5\) | \(4\) | $-$ | $-$ | $-$ | \(q-8q^{3}+5q^{5}+4q^{7}+37q^{9}-20q^{11}+\cdots\) | |
740.4.a.b | $5$ | $43.661$ | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) | None | \(0\) | \(4\) | \(25\) | \(-11\) | $-$ | $-$ | $-$ | \(q+(1-\beta _{1})q^{3}+5q^{5}+(-3+2\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\) | |
740.4.a.c | $8$ | $43.661$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(0\) | \(-40\) | \(7\) | $-$ | $+$ | $+$ | \(q+\beta _{1}q^{3}-5q^{5}+(1+\beta _{6})q^{7}+(7+\beta _{2}+\cdots)q^{9}+\cdots\) | |
740.4.a.d | $11$ | $43.661$ | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) | None | \(0\) | \(2\) | \(55\) | \(-7\) | $-$ | $-$ | $+$ | \(q+\beta _{1}q^{3}+5q^{5}+(-1-\beta _{6})q^{7}+(15+\cdots)q^{9}+\cdots\) | |
740.4.a.e | $11$ | $43.661$ | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) | None | \(0\) | \(6\) | \(-55\) | \(7\) | $-$ | $+$ | $-$ | \(q+(1-\beta _{1})q^{3}-5q^{5}+(1+\beta _{5})q^{7}+(12+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(740))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(740)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(185))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(370))\)\(^{\oplus 2}\)