Defining parameters
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(18\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(49))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 18 | 13 | 5 |
Cusp forms | 10 | 8 | 2 |
Eisenstein series | 8 | 5 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(7\) | Dim |
---|---|
\(+\) | \(5\) |
\(-\) | \(3\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(49))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 7 | |||||||
49.4.a.a | $1$ | $2.891$ | \(\Q\) | \(\Q(\sqrt{-7}) \) | \(-5\) | \(0\) | \(0\) | \(0\) | $-$ | \(q-5q^{2}+17q^{4}-45q^{8}-3^{3}q^{9}-68q^{11}+\cdots\) | |
49.4.a.b | $1$ | $2.891$ | \(\Q\) | None | \(-1\) | \(2\) | \(-16\) | \(0\) | $-$ | \(q-q^{2}+2q^{3}-7q^{4}-2^{4}q^{5}-2q^{6}+\cdots\) | |
49.4.a.c | $1$ | $2.891$ | \(\Q\) | None | \(2\) | \(-7\) | \(-7\) | \(0\) | $-$ | \(q+2q^{2}-7q^{3}-4q^{4}-7q^{5}-14q^{6}+\cdots\) | |
49.4.a.d | $1$ | $2.891$ | \(\Q\) | None | \(2\) | \(7\) | \(7\) | \(0\) | $+$ | \(q+2q^{2}+7q^{3}-4q^{4}+7q^{5}+14q^{6}+\cdots\) | |
49.4.a.e | $4$ | $2.891$ | \(\Q(\sqrt{2}, \sqrt{65})\) | None | \(2\) | \(0\) | \(0\) | \(0\) | $+$ | \(q+(1+\beta _{1})q^{2}+\beta _{2}q^{3}+(9+\beta _{1})q^{4}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(49))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(49)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)