Defining parameters
Level: | \( N \) | \(=\) | \( 1075 = 5^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1075.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 12 \) | ||
Sturm bound: | \(660\) | ||
Trace bound: | \(8\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(1075))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 556 | 332 | 224 |
Cusp forms | 544 | 332 | 212 |
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.
\(5\) | \(43\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(76\) |
\(+\) | \(-\) | $-$ | \(82\) |
\(-\) | \(+\) | $-$ | \(89\) |
\(-\) | \(-\) | $+$ | \(85\) |
Plus space | \(+\) | \(161\) | |
Minus space | \(-\) | \(171\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(1075))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 5 | 43 | |||||||
1075.6.a.a | $8$ | $172.413$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(12\) | \(26\) | \(0\) | \(136\) | $+$ | $-$ | \(q+(2-\beta _{1})q^{2}+(2+\beta _{1}-\beta _{4}+\beta _{7})q^{3}+\cdots\) | |
1075.6.a.b | $10$ | $172.413$ | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) | None | \(-8\) | \(-28\) | \(0\) | \(-60\) | $+$ | $+$ | \(q+(-1+\beta _{1})q^{2}+(-3-\beta _{6})q^{3}+(21+\cdots)q^{4}+\cdots\) | |
1075.6.a.c | $13$ | $172.413$ | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) | None | \(7\) | \(16\) | \(0\) | \(372\) | $+$ | $+$ | \(q+(1-\beta _{1})q^{2}+(1+\beta _{3})q^{3}+(9+\beta _{2}+\cdots)q^{4}+\cdots\) | |
1075.6.a.d | $15$ | $172.413$ | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) | None | \(5\) | \(20\) | \(0\) | \(118\) | $+$ | $-$ | \(q+\beta _{1}q^{2}+(1-\beta _{6})q^{3}+(14+\beta _{2})q^{4}+\cdots\) | |
1075.6.a.e | $20$ | $172.413$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(-7\) | \(-16\) | \(0\) | \(-372\) | $+$ | $+$ | \(q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(17+\beta _{1}+\cdots)q^{4}+\cdots\) | |
1075.6.a.f | $22$ | $172.413$ | None | \(-5\) | \(-20\) | \(0\) | \(-118\) | $+$ | $-$ | |||
1075.6.a.g | $33$ | $172.413$ | None | \(0\) | \(0\) | \(0\) | \(0\) | $-$ | $-$ | |||
1075.6.a.h | $33$ | $172.413$ | None | \(0\) | \(0\) | \(0\) | \(0\) | $+$ | $+$ | |||
1075.6.a.i | $37$ | $172.413$ | None | \(0\) | \(0\) | \(0\) | \(0\) | $-$ | $+$ | |||
1075.6.a.j | $37$ | $172.413$ | None | \(0\) | \(0\) | \(0\) | \(0\) | $+$ | $-$ | |||
1075.6.a.k | $52$ | $172.413$ | None | \(-20\) | \(-54\) | \(0\) | \(-196\) | $-$ | $-$ | |||
1075.6.a.l | $52$ | $172.413$ | None | \(20\) | \(54\) | \(0\) | \(196\) | $-$ | $+$ |
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(1075))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_0(1075)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(215))\)\(^{\oplus 2}\)