Defining parameters
| Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1045.a (trivial) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 9 \) | ||
| Sturm bound: | \(480\) | ||
| Trace bound: | \(2\) | ||
| Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1045))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 364 | 180 | 184 |
| Cusp forms | 356 | 180 | 176 |
| 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.
| \(5\) | \(11\) | \(19\) | Fricke | Dim. |
|---|---|---|---|---|
| \(+\) | \(+\) | \(+\) | \(+\) | \(23\) |
| \(+\) | \(+\) | \(-\) | \(-\) | \(21\) |
| \(+\) | \(-\) | \(+\) | \(-\) | \(23\) |
| \(+\) | \(-\) | \(-\) | \(+\) | \(25\) |
| \(-\) | \(+\) | \(+\) | \(-\) | \(22\) |
| \(-\) | \(+\) | \(-\) | \(+\) | \(24\) |
| \(-\) | \(-\) | \(+\) | \(+\) | \(22\) |
| \(-\) | \(-\) | \(-\) | \(-\) | \(20\) |
| Plus space | \(+\) | \(94\) | ||
| Minus space | \(-\) | \(86\) | ||
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1045))\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 5 | 11 | 19 | |||||||
| 1045.4.a.a | $1$ | $61.657$ | \(\Q\) | None | \(-5\) | \(-1\) | \(-5\) | \(-2\) | $+$ | $+$ | $-$ | \(q-5q^{2}-q^{3}+17q^{4}-5q^{5}+5q^{6}+\cdots\) | |
| 1045.4.a.b | $20$ | $61.657$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(-12\) | \(-21\) | \(100\) | \(-131\) | $-$ | $-$ | $-$ | \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{5})q^{3}+(4+\cdots)q^{4}+\cdots\) | |
| 1045.4.a.c | $20$ | $61.657$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(-1\) | \(-8\) | \(-100\) | \(49\) | $+$ | $+$ | $-$ | \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(3+\beta _{2})q^{4}-5q^{5}+\cdots\) | |
| 1045.4.a.d | $22$ | $61.657$ | None | \(-4\) | \(-21\) | \(110\) | \(-41\) | $-$ | $+$ | $+$ | |||
| 1045.4.a.e | $22$ | $61.657$ | None | \(12\) | \(21\) | \(110\) | \(93\) | $-$ | $-$ | $+$ | |||
| 1045.4.a.f | $23$ | $61.657$ | None | \(-2\) | \(-9\) | \(-115\) | \(13\) | $+$ | $-$ | $+$ | |||
| 1045.4.a.g | $23$ | $61.657$ | None | \(6\) | \(9\) | \(-115\) | \(-37\) | $+$ | $+$ | $+$ | |||
| 1045.4.a.h | $24$ | $61.657$ | None | \(4\) | \(21\) | \(120\) | \(71\) | $-$ | $+$ | $-$ | |||
| 1045.4.a.i | $25$ | $61.657$ | None | \(2\) | \(9\) | \(-125\) | \(-15\) | $+$ | $-$ | $-$ | |||
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1045))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(1045)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 2}\)