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Properties

Label 33.3.b
Level $33$
Weight $3$
Character orbit 33.b
Rep. character $\chi_{33}(23,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $12$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 33.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(33, [\chi])\).

Total New Old
Modular forms 10 6 4
Cusp forms 6 6 0
Eisenstein series 4 0 4

Trace form

\( 6 q + q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 11 q^{9} + O(q^{10}) \) \( 6 q + q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 11 q^{9} + 36 q^{10} - 28 q^{12} + 13 q^{15} - 12 q^{16} + 38 q^{18} - 48 q^{19} - 86 q^{21} + 24 q^{24} + 48 q^{25} + 34 q^{27} + 48 q^{28} + 142 q^{30} - 6 q^{31} - 11 q^{33} + 24 q^{34} - 212 q^{36} - 30 q^{37} - 32 q^{39} - 168 q^{40} - 68 q^{42} + 180 q^{43} + 17 q^{45} - 132 q^{46} + 140 q^{48} - 30 q^{49} + 214 q^{51} - 192 q^{52} - 176 q^{54} + 66 q^{55} + 108 q^{57} + 480 q^{58} + 56 q^{60} + 14 q^{63} + 228 q^{64} - 110 q^{66} - 54 q^{67} - 253 q^{69} - 360 q^{70} + 72 q^{72} - 432 q^{73} - 238 q^{75} + 264 q^{76} - 128 q^{78} - 156 q^{79} + 275 q^{81} - 48 q^{82} + 416 q^{84} + 108 q^{85} - 252 q^{87} + 132 q^{88} + 410 q^{90} + 192 q^{91} - 131 q^{93} - 312 q^{94} + 272 q^{96} + 342 q^{97} - 55 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(33, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
33.3.b.a 33.b 3.b $2$ $0.899$ \(\Q(\sqrt{-11}) \) None \(0\) \(6\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{2}+3q^{3}-7q^{4}+2\beta q^{5}-3\beta q^{6}+\cdots\)
33.3.b.b 33.b 3.b $4$ $0.899$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-5\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-1+\beta _{1}+\cdots)q^{3}+\cdots\)