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

\( 6 q - 4 q^{2} + 44 q^{4} - 16 q^{5} - 12 q^{6} - 32 q^{7} + 36 q^{8} + 54 q^{9} + O(q^{10}) \) \( 6 q - 4 q^{2} + 44 q^{4} - 16 q^{5} - 12 q^{6} - 32 q^{7} + 36 q^{8} + 54 q^{9} - 88 q^{10} - 24 q^{12} - 116 q^{13} - 28 q^{14} + 60 q^{15} + 212 q^{16} + 152 q^{17} - 36 q^{18} + 8 q^{19} - 596 q^{20} - 84 q^{21} + 44 q^{22} + 244 q^{23} - 324 q^{24} + 146 q^{25} + 428 q^{26} - 192 q^{28} - 120 q^{29} + 336 q^{30} + 160 q^{31} + 364 q^{32} + 66 q^{33} - 208 q^{34} + 920 q^{35} + 396 q^{36} - 268 q^{37} - 696 q^{38} - 336 q^{39} - 168 q^{40} - 760 q^{41} + 852 q^{42} + 200 q^{43} - 616 q^{44} - 144 q^{45} - 464 q^{46} - 644 q^{47} - 816 q^{48} + 774 q^{49} + 148 q^{50} - 624 q^{51} + 264 q^{52} - 696 q^{53} - 108 q^{54} + 440 q^{55} + 228 q^{56} + 84 q^{57} + 840 q^{58} + 40 q^{59} + 12 q^{60} - 1180 q^{61} + 3032 q^{62} - 288 q^{63} + 1068 q^{64} - 880 q^{65} + 264 q^{66} - 1344 q^{67} + 1000 q^{68} + 1020 q^{69} - 2296 q^{70} + 756 q^{71} + 324 q^{72} + 724 q^{73} + 2256 q^{74} + 840 q^{75} + 2048 q^{76} - 176 q^{77} + 420 q^{78} - 144 q^{79} - 5732 q^{80} + 486 q^{81} - 2176 q^{82} + 264 q^{83} - 2880 q^{84} - 1840 q^{85} - 288 q^{86} + 1368 q^{87} + 132 q^{88} - 180 q^{89} - 792 q^{90} + 1680 q^{91} + 4268 q^{92} - 1632 q^{93} + 5104 q^{94} - 168 q^{95} - 3084 q^{96} - 2148 q^{97} - 8580 q^{98} + O(q^{100}) \)

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

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

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

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