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Properties

Label 33.3.g
Level $33$
Weight $3$
Character orbit 33.g
Rep. character $\chi_{33}(7,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $16$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 33.g (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 40 16 24
Cusp forms 24 16 8
Eisenstein series 16 0 16

Trace form

\( 16 q + 20 q^{4} - 4 q^{5} - 30 q^{7} - 40 q^{8} - 12 q^{9} + O(q^{10}) \) \( 16 q + 20 q^{4} - 4 q^{5} - 30 q^{7} - 40 q^{8} - 12 q^{9} - 10 q^{11} - 24 q^{12} + 30 q^{13} - 2 q^{14} - 24 q^{15} + 16 q^{16} - 10 q^{17} - 30 q^{18} + 42 q^{20} + 42 q^{22} + 132 q^{23} + 90 q^{24} - 2 q^{25} + 46 q^{26} - 50 q^{28} + 160 q^{29} + 180 q^{30} + 10 q^{31} + 12 q^{33} - 368 q^{34} - 320 q^{35} + 60 q^{36} - 126 q^{37} - 130 q^{38} + 30 q^{40} - 120 q^{41} - 204 q^{42} - 206 q^{44} - 12 q^{45} + 50 q^{46} - 150 q^{47} - 96 q^{48} + 210 q^{49} + 330 q^{50} - 60 q^{51} + 110 q^{52} + 342 q^{53} + 244 q^{55} + 524 q^{56} + 60 q^{57} + 150 q^{58} + 110 q^{59} + 36 q^{60} - 90 q^{61} + 40 q^{62} + 90 q^{63} - 168 q^{64} + 48 q^{66} + 36 q^{67} + 80 q^{68} + 210 q^{69} + 340 q^{70} - 236 q^{71} - 150 q^{72} - 350 q^{73} - 730 q^{74} - 408 q^{75} - 390 q^{77} - 312 q^{78} + 210 q^{79} - 806 q^{80} - 36 q^{81} + 114 q^{82} - 190 q^{83} - 180 q^{84} + 110 q^{85} + 736 q^{86} + 144 q^{88} + 76 q^{89} + 60 q^{90} + 306 q^{91} - 150 q^{92} + 144 q^{93} - 350 q^{94} + 430 q^{95} + 450 q^{96} - 354 q^{97} + 180 q^{99} + O(q^{100}) \)

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.g.a 33.g 11.d $16$ $0.899$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-4\) \(-30\) $\mathrm{SU}(2)[C_{10}]$ \(q+(1+\beta _{2}-\beta _{5}+\beta _{7}+\beta _{8})q^{2}-\beta _{14}q^{3}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(33, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(33, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)