Defining parameters
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(51\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_0(10))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 51 | 11 | 40 |
Cusp forms | 47 | 11 | 36 |
Eisenstein series | 4 | 0 | 4 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(5\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(3\) |
\(+\) | \(-\) | \(-\) | \(3\) |
\(-\) | \(+\) | \(-\) | \(3\) |
\(-\) | \(-\) | \(+\) | \(2\) |
Plus space | \(+\) | \(5\) | |
Minus space | \(-\) | \(6\) |
Trace form
Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_0(10))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 5 | |||||||
10.34.a.a | $2$ | $68.983$ | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) | None | \(131072\) | \(-74648412\) | \(305175781250\) | \(20\!\cdots\!56\) | $-$ | $-$ | \(q+2^{16}q^{2}+(-37324206-3\beta )q^{3}+\cdots\) | |
10.34.a.b | $3$ | $68.983$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(-196608\) | \(-33025382\) | \(-457763671875\) | \(39\!\cdots\!66\) | $+$ | $+$ | \(q-2^{16}q^{2}+(-11008461-\beta _{1})q^{3}+\cdots\) | |
10.34.a.c | $3$ | $68.983$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(-196608\) | \(156523368\) | \(457763671875\) | \(-86\!\cdots\!84\) | $+$ | $-$ | \(q-2^{16}q^{2}+(52174456-\beta _{1})q^{3}+2^{32}q^{4}+\cdots\) | |
10.34.a.d | $3$ | $68.983$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(196608\) | \(25718682\) | \(-457763671875\) | \(-28\!\cdots\!66\) | $-$ | $+$ | \(q+2^{16}q^{2}+(8572894-\beta _{1})q^{3}+2^{32}q^{4}+\cdots\) |
Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_0(10))\) into lower level spaces
\( S_{34}^{\mathrm{old}}(\Gamma_0(10)) \simeq \) \(S_{34}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)