Properties

Label 33.6.e
Level $33$
Weight $6$
Character orbit 33.e
Rep. character $\chi_{33}(4,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $40$
Newform subspaces $2$
Sturm bound $24$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 33.e (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(33, [\chi])\).

Total New Old
Modular forms 88 40 48
Cusp forms 72 40 32
Eisenstein series 16 0 16

Trace form

\( 40q + 4q^{2} - 116q^{4} - 44q^{5} - 72q^{6} - 474q^{7} - 548q^{8} - 810q^{9} + O(q^{10}) \) \( 40q + 4q^{2} - 116q^{4} - 44q^{5} - 72q^{6} - 474q^{7} - 548q^{8} - 810q^{9} + 1528q^{10} + 1454q^{11} + 792q^{12} - 1806q^{13} - 998q^{14} - 198q^{15} - 8576q^{16} - 662q^{17} - 486q^{18} + 2028q^{19} + 11214q^{20} + 7056q^{21} + 10154q^{22} + 9540q^{23} - 3294q^{24} - 22508q^{25} - 10486q^{26} + 6066q^{28} - 15716q^{29} + 6804q^{30} + 14748q^{31} + 64488q^{32} + 7254q^{33} + 7456q^{34} - 65472q^{35} - 9396q^{36} - 28326q^{37} - 54026q^{38} - 1008q^{39} - 30434q^{40} + 46852q^{41} + 54612q^{42} + 41936q^{43} + 82886q^{44} - 3564q^{45} - 50526q^{46} - 91418q^{47} - 55440q^{48} - 84520q^{49} - 56634q^{50} + 7776q^{51} + 28902q^{52} - 94834q^{53} + 23328q^{54} + 15344q^{55} + 338532q^{56} + 13608q^{57} + 94646q^{58} - 6682q^{59} - 43740q^{60} + 67482q^{61} - 39272q^{62} - 38394q^{63} + 42608q^{64} - 162404q^{65} - 81432q^{66} + 30908q^{67} - 33128q^{68} + 113670q^{69} - 119324q^{70} + 308052q^{71} + 53622q^{72} + 87744q^{73} - 42114q^{74} - 87192q^{75} + 126080q^{76} - 311374q^{77} - 432720q^{78} + 77682q^{79} - 89422q^{80} - 65610q^{81} + 240530q^{82} + 12290q^{83} + 253692q^{84} - 72334q^{85} - 37688q^{86} + 401976q^{87} - 569152q^{88} + 387124q^{89} + 76788q^{90} + 679174q^{91} + 716510q^{92} + 33012q^{93} + 11222q^{94} - 243210q^{95} - 359010q^{96} - 445650q^{97} - 2446744q^{98} - 198936q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(33, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
33.6.e.a \(20\) \(5.293\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(-45\) \(-33\) \(-335\) \(q+(-\beta _{1}+\beta _{7})q^{2}-9\beta _{9}q^{3}+(-\beta _{6}+\cdots)q^{4}+\cdots\)
33.6.e.b \(20\) \(5.293\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(6\) \(45\) \(-11\) \(-139\) \(q+(-\beta _{5}+\beta _{6})q^{2}+9\beta _{7}q^{3}+(-12+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(33, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(33, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)