Properties

Label 9.6.a
Level 9
Weight 6
Character orbit a
Rep. character \(\chi_{9}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 9.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(9))\).

Total New Old
Modular forms 7 2 5
Cusp forms 3 1 2
Eisenstein series 4 1 3

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

\( q + 6q^{2} + 4q^{4} - 6q^{5} - 40q^{7} - 168q^{8} + O(q^{10}) \) \( q + 6q^{2} + 4q^{4} - 6q^{5} - 40q^{7} - 168q^{8} - 36q^{10} + 564q^{11} + 638q^{13} - 240q^{14} - 1136q^{16} - 882q^{17} - 556q^{19} - 24q^{20} + 3384q^{22} + 840q^{23} - 3089q^{25} + 3828q^{26} - 160q^{28} - 4638q^{29} + 4400q^{31} - 1440q^{32} - 5292q^{34} + 240q^{35} - 2410q^{37} - 3336q^{38} + 1008q^{40} + 6870q^{41} + 9644q^{43} + 2256q^{44} + 5040q^{46} + 18672q^{47} - 15207q^{49} - 18534q^{50} + 2552q^{52} - 33750q^{53} - 3384q^{55} + 6720q^{56} - 27828q^{58} + 18084q^{59} + 39758q^{61} + 26400q^{62} + 27712q^{64} - 3828q^{65} - 23068q^{67} - 3528q^{68} + 1440q^{70} + 4248q^{71} - 41110q^{73} - 14460q^{74} - 2224q^{76} - 22560q^{77} + 21920q^{79} + 6816q^{80} + 41220q^{82} - 82452q^{83} + 5292q^{85} + 57864q^{86} - 94752q^{88} + 94086q^{89} - 25520q^{91} + 3360q^{92} + 112032q^{94} + 3336q^{95} + 49442q^{97} - 91242q^{98} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(9))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3
9.6.a.a \(1\) \(1.443\) \(\Q\) None \(6\) \(0\) \(-6\) \(-40\) \(-\) \(q+6q^{2}+4q^{4}-6q^{5}-40q^{7}-168q^{8}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(9))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(9)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)