Defining parameters
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(33))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 54 | 20 | 34 |
Cusp forms | 50 | 20 | 30 |
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.
\(3\) | \(11\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(5\) |
\(+\) | \(-\) | $-$ | \(6\) |
\(-\) | \(+\) | $-$ | \(5\) |
\(-\) | \(-\) | $+$ | \(4\) |
Plus space | \(+\) | \(9\) | |
Minus space | \(-\) | \(11\) |
Trace form
Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(33))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 11 | |||||||
33.14.a.a | $1$ | $35.386$ | \(\Q\) | None | \(140\) | \(729\) | \(48740\) | \(487486\) | $-$ | $+$ | \(q+140q^{2}+3^{6}q^{3}+11408q^{4}+48740q^{5}+\cdots\) | |
33.14.a.b | $4$ | $35.386$ | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) | None | \(-11\) | \(2916\) | \(-83432\) | \(69652\) | $-$ | $-$ | \(q+(-3+\beta _{1})q^{2}+3^{6}q^{3}+(-1564+\cdots)q^{4}+\cdots\) | |
33.14.a.c | $4$ | $35.386$ | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) | None | \(41\) | \(2916\) | \(-38422\) | \(41998\) | $-$ | $+$ | \(q+(10+\beta _{1})q^{2}+3^{6}q^{3}+(5909+43\beta _{1}+\cdots)q^{4}+\cdots\) | |
33.14.a.d | $5$ | $35.386$ | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) | None | \(-53\) | \(-3645\) | \(10318\) | \(-667804\) | $+$ | $+$ | \(q+(-11+\beta _{1})q^{2}-3^{6}q^{3}+(7020-11\beta _{1}+\cdots)q^{4}+\cdots\) | |
33.14.a.e | $6$ | $35.386$ | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) | None | \(11\) | \(-4374\) | \(-20932\) | \(284152\) | $+$ | $-$ | \(q+(2-\beta _{1})q^{2}-3^{6}q^{3}+(3061-10\beta _{1}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(33))\) into lower level spaces
\( S_{14}^{\mathrm{old}}(\Gamma_0(33)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)