Properties

Label 33.4.a
Level $33$
Weight $4$
Character orbit 33.a
Rep. character $\chi_{33}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $4$
Sturm bound $16$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 33.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(16\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(33))\).

Total New Old
Modular forms 14 6 8
Cusp forms 10 6 4
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.

\(3\)\(11\)FrickeDim
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(2\)

Trace form

\( 6 q - 4 q^{2} + 44 q^{4} - 16 q^{5} - 12 q^{6} - 32 q^{7} + 36 q^{8} + 54 q^{9} - 88 q^{10} - 24 q^{12} - 116 q^{13} - 28 q^{14} + 60 q^{15} + 212 q^{16} + 152 q^{17} - 36 q^{18} + 8 q^{19} - 596 q^{20}+ \cdots - 8580 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(33))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 11
33.4.a.a 33.a 1.a $1$ $1.947$ \(\Q\) None 33.4.a.a \(-5\) \(3\) \(-14\) \(-32\) $-$ $+$ $\mathrm{SU}(2)$ \(q-5q^{2}+3q^{3}+17q^{4}-14q^{5}-15q^{6}+\cdots\)
33.4.a.b 33.a 1.a $1$ $1.947$ \(\Q\) None 33.4.a.b \(-1\) \(-3\) \(-4\) \(-26\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}-7q^{4}-4q^{5}+3q^{6}+\cdots\)
33.4.a.c 33.a 1.a $2$ $1.947$ \(\Q(\sqrt{97}) \) None 33.4.a.c \(1\) \(-6\) \(-14\) \(24\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-3q^{3}+(2^{4}+\beta )q^{4}+(-6-2\beta )q^{5}+\cdots\)
33.4.a.d 33.a 1.a $2$ $1.947$ \(\Q(\sqrt{33}) \) None 33.4.a.d \(1\) \(6\) \(16\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+3q^{3}+\beta q^{4}+(10-4\beta )q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(33))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(33)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)