Properties

Label 3.10.a
Level 3
Weight 10
Character orbit a
Rep. character \(\chi_{3}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 2
Sturm bound 3
Trace bound 2

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 3.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(3\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(3))\).

Total New Old
Modular forms 4 2 2
Cusp forms 2 2 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.

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

Trace form

\( 2q - 18q^{2} + 596q^{4} - 2844q^{5} + 4374q^{6} + 4648q^{7} - 22392q^{8} + 13122q^{9} + O(q^{10}) \) \( 2q - 18q^{2} + 596q^{4} - 2844q^{5} + 4374q^{6} + 4648q^{7} - 22392q^{8} + 13122q^{9} + 19764q^{10} + 22608q^{11} - 78732q^{12} - 120308q^{13} + 325584q^{14} - 17496q^{15} - 179440q^{16} - 171180q^{17} - 118098q^{18} + 737104q^{19} - 742536q^{20} + 1102248q^{21} + 327240q^{22} - 2732976q^{23} - 227448q^{24} + 161246q^{25} + 6016644q^{26} - 5228384q^{28} - 1950012q^{29} - 6062364q^{30} + 6701512q^{31} + 10875168q^{32} + 1592136q^{33} - 8921988q^{34} - 8079120q^{35} + 3910356q^{36} + 1874668q^{37} - 18758664q^{38} + 14801616q^{39} + 32144688q^{40} - 11576988q^{41} + 244944q^{42} - 27506192q^{43} - 2815632q^{44} - 18659484q^{45} + 3158352q^{46} + 51281136q^{47} - 6613488q^{48} + 22683570q^{49} + 15134994q^{50} - 31387824q^{51} - 124661480q^{52} + 94588884q^{53} + 28697814q^{54} - 34271424q^{55} - 71144640q^{56} - 36374184q^{57} + 323595972q^{58} - 106386624q^{59} + 106743096q^{60} - 147126020q^{61} - 261185184q^{62} + 30495528q^{63} - 78156736q^{64} + 151342488q^{65} + 35114472q^{66} + 374059840q^{67} + 137315304q^{68} - 64315296q^{69} - 463307040q^{70} - 80513136q^{71} - 146913912q^{72} - 270650156q^{73} + 437254164q^{74} + 49758624q^{75} + 437902096q^{76} + 186280416q^{77} - 396328140q^{78} - 209879960q^{79} + 263981664q^{80} + 86093442q^{81} + 26522316q^{82} - 1020687984q^{83} + 145496736q^{84} + 285268392q^{85} - 259740792q^{86} + 918137592q^{87} - 280716192q^{88} + 90873684q^{89} + 129671604q^{90} + 963739952q^{91} - 428535072q^{92} - 602614728q^{93} - 605638944q^{94} - 999662976q^{95} - 216460512q^{96} + 339473380q^{97} + 1503597438q^{98} + 148331088q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(3))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3
3.10.a.a \(1\) \(1.545\) \(\Q\) None \(-36\) \(-81\) \(-1314\) \(-4480\) \(+\) \(q-6^{2}q^{2}-3^{4}q^{3}+28^{2}q^{4}-1314q^{5}+\cdots\)
3.10.a.b \(1\) \(1.545\) \(\Q\) None \(18\) \(81\) \(-1530\) \(9128\) \(-\) \(q+18q^{2}+3^{4}q^{3}-188q^{4}-1530q^{5}+\cdots\)