Properties

Label 3.10
Level 3
Weight 10
Dimension 2
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(3))\).

Total New Old
Modular forms 4 2 2
Cusp forms 2 2 0
Eisenstein series 2 0 2

Trace form

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

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3.10.a \(\chi_{3}(1, \cdot)\) 3.10.a.a 1 1
3.10.a.b 1