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Properties

Label 3.6.a
Level $3$
Weight $6$
Character orbit 3.a
Rep. character $\chi_{3}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $2$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 3.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(3))\).

Total New Old
Modular forms 3 1 2
Cusp forms 1 1 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)Dim.
\(-\)\(1\)

Trace form

\( q - 6q^{2} + 9q^{3} + 4q^{4} + 6q^{5} - 54q^{6} - 40q^{7} + 168q^{8} + 81q^{9} + O(q^{10}) \) \( q - 6q^{2} + 9q^{3} + 4q^{4} + 6q^{5} - 54q^{6} - 40q^{7} + 168q^{8} + 81q^{9} - 36q^{10} - 564q^{11} + 36q^{12} + 638q^{13} + 240q^{14} + 54q^{15} - 1136q^{16} + 882q^{17} - 486q^{18} - 556q^{19} + 24q^{20} - 360q^{21} + 3384q^{22} - 840q^{23} + 1512q^{24} - 3089q^{25} - 3828q^{26} + 729q^{27} - 160q^{28} + 4638q^{29} - 324q^{30} + 4400q^{31} + 1440q^{32} - 5076q^{33} - 5292q^{34} - 240q^{35} + 324q^{36} - 2410q^{37} + 3336q^{38} + 5742q^{39} + 1008q^{40} - 6870q^{41} + 2160q^{42} + 9644q^{43} - 2256q^{44} + 486q^{45} + 5040q^{46} - 18672q^{47} - 10224q^{48} - 15207q^{49} + 18534q^{50} + 7938q^{51} + 2552q^{52} + 33750q^{53} - 4374q^{54} - 3384q^{55} - 6720q^{56} - 5004q^{57} - 27828q^{58} - 18084q^{59} + 216q^{60} + 39758q^{61} - 26400q^{62} - 3240q^{63} + 27712q^{64} + 3828q^{65} + 30456q^{66} - 23068q^{67} + 3528q^{68} - 7560q^{69} + 1440q^{70} - 4248q^{71} + 13608q^{72} - 41110q^{73} + 14460q^{74} - 27801q^{75} - 2224q^{76} + 22560q^{77} - 34452q^{78} + 21920q^{79} - 6816q^{80} + 6561q^{81} + 41220q^{82} + 82452q^{83} - 1440q^{84} + 5292q^{85} - 57864q^{86} + 41742q^{87} - 94752q^{88} - 94086q^{89} - 2916q^{90} - 25520q^{91} - 3360q^{92} + 39600q^{93} + 112032q^{94} - 3336q^{95} + 12960q^{96} + 49442q^{97} + 91242q^{98} - 45684q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3
3.6.a.a \(1\) \(0.481\) \(\Q\) None \(-6\) \(9\) \(6\) \(-40\) \(-\) \(q-6q^{2}+9q^{3}+4q^{4}+6q^{5}-54q^{6}+\cdots\)