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

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

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

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