Properties

Label 33.6.a
Level $33$
Weight $6$
Character orbit 33.a
Rep. character $\chi_{33}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $5$
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.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(24\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(33))\).

Total New Old
Modular forms 22 8 14
Cusp forms 18 8 10
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.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(3\)
Minus space\(-\)\(5\)

Trace form

\( 8q + 8q^{2} - 18q^{3} + 108q^{4} + 32q^{5} + 180q^{6} - 36q^{7} - 108q^{8} + 648q^{9} + O(q^{10}) \) \( 8q + 8q^{2} - 18q^{3} + 108q^{4} + 32q^{5} + 180q^{6} - 36q^{7} - 108q^{8} + 648q^{9} + 544q^{10} - 864q^{12} - 480q^{13} + 1508q^{14} - 900q^{15} + 948q^{16} - 4612q^{17} + 648q^{18} - 916q^{19} + 5788q^{20} + 2484q^{21} - 968q^{22} - 2480q^{23} + 540q^{24} + 15816q^{25} - 14308q^{26} - 1458q^{27} - 24176q^{28} - 6180q^{29} - 2736q^{30} + 1752q^{31} + 13612q^{32} - 2178q^{33} - 3392q^{34} + 9992q^{35} + 8748q^{36} - 27904q^{37} + 8304q^{38} - 10476q^{39} + 10968q^{40} + 39188q^{41} - 15372q^{42} + 30356q^{43} - 4840q^{44} + 2592q^{45} + 54896q^{46} + 68152q^{47} + 12528q^{48} + 12744q^{49} - 137624q^{50} + 2448q^{51} - 20696q^{52} - 16776q^{53} + 14580q^{54} - 24200q^{55} + 5508q^{56} + 32220q^{57} + 7320q^{58} + 33280q^{59} - 20052q^{60} - 51208q^{61} + 49592q^{62} - 2916q^{63} - 180532q^{64} - 128992q^{65} - 17424q^{66} + 58648q^{67} - 111848q^{68} - 10440q^{69} + 217864q^{70} + 35064q^{71} - 8748q^{72} + 30456q^{73} + 23304q^{74} - 98766q^{75} - 117712q^{76} + 29524q^{77} + 123084q^{78} - 128372q^{79} + 59164q^{80} + 52488q^{81} + 86560q^{82} + 51576q^{83} + 41328q^{84} + 87160q^{85} + 220296q^{86} - 31320q^{87} + 68244q^{88} + 40368q^{89} + 44064q^{90} + 42536q^{91} + 210140q^{92} - 118152q^{93} - 128896q^{94} - 234168q^{95} - 44460q^{96} - 267584q^{97} - 228120q^{98} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(33))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 11
33.6.a.a \(1\) \(5.293\) \(\Q\) None \(-2\) \(-9\) \(46\) \(148\) \(+\) \(-\) \(q-2q^{2}-9q^{3}-28q^{4}+46q^{5}+18q^{6}+\cdots\)
33.6.a.b \(1\) \(5.293\) \(\Q\) None \(1\) \(9\) \(-92\) \(-26\) \(-\) \(-\) \(q+q^{2}+9q^{3}-31q^{4}-92q^{5}+9q^{6}+\cdots\)
33.6.a.c \(2\) \(5.293\) \(\Q(\sqrt{177}) \) None \(-5\) \(-18\) \(58\) \(-286\) \(+\) \(+\) \(q+(-2-\beta )q^{2}-9q^{3}+(2^{4}+5\beta )q^{4}+\cdots\)
33.6.a.d \(2\) \(5.293\) \(\Q(\sqrt{313}) \) None \(1\) \(-18\) \(-38\) \(-18\) \(+\) \(-\) \(q+\beta q^{2}-9q^{3}+(46+\beta )q^{4}+(-24+\cdots)q^{5}+\cdots\)
33.6.a.e \(2\) \(5.293\) \(\Q(\sqrt{33}) \) None \(13\) \(18\) \(58\) \(146\) \(-\) \(+\) \(q+(7-\beta )q^{2}+9q^{3}+(5^{2}-13\beta )q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(33))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(33)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)