Properties

Label 23.3
Level 23
Weight 3
Dimension 33
Nonzero newspaces 2
Newforms 2
Sturm bound 132
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 2 \)
Sturm bound: \(132\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(23))\).

Total New Old
Modular forms 55 55 0
Cusp forms 33 33 0
Eisenstein series 22 22 0

Trace form

\(33q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut -\mathstrut 11q^{4} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 11q^{8} \) \(\mathstrut -\mathstrut 11q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(33q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut -\mathstrut 11q^{4} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 11q^{8} \) \(\mathstrut -\mathstrut 11q^{9} \) \(\mathstrut -\mathstrut 11q^{10} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 11q^{13} \) \(\mathstrut -\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 121q^{16} \) \(\mathstrut +\mathstrut 44q^{17} \) \(\mathstrut +\mathstrut 165q^{18} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut +\mathstrut 77q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut -\mathstrut 33q^{23} \) \(\mathstrut -\mathstrut 154q^{24} \) \(\mathstrut -\mathstrut 77q^{25} \) \(\mathstrut -\mathstrut 99q^{26} \) \(\mathstrut -\mathstrut 176q^{27} \) \(\mathstrut -\mathstrut 275q^{28} \) \(\mathstrut -\mathstrut 88q^{29} \) \(\mathstrut -\mathstrut 363q^{30} \) \(\mathstrut -\mathstrut 110q^{31} \) \(\mathstrut -\mathstrut 231q^{32} \) \(\mathstrut -\mathstrut 132q^{33} \) \(\mathstrut +\mathstrut 231q^{34} \) \(\mathstrut +\mathstrut 209q^{35} \) \(\mathstrut +\mathstrut 484q^{36} \) \(\mathstrut +\mathstrut 341q^{37} \) \(\mathstrut +\mathstrut 374q^{38} \) \(\mathstrut +\mathstrut 253q^{39} \) \(\mathstrut +\mathstrut 429q^{40} \) \(\mathstrut +\mathstrut 77q^{41} \) \(\mathstrut +\mathstrut 319q^{42} \) \(\mathstrut +\mathstrut 77q^{43} \) \(\mathstrut +\mathstrut 110q^{44} \) \(\mathstrut -\mathstrut 99q^{46} \) \(\mathstrut -\mathstrut 110q^{47} \) \(\mathstrut -\mathstrut 319q^{48} \) \(\mathstrut -\mathstrut 275q^{49} \) \(\mathstrut -\mathstrut 396q^{50} \) \(\mathstrut -\mathstrut 275q^{51} \) \(\mathstrut -\mathstrut 781q^{52} \) \(\mathstrut -\mathstrut 187q^{53} \) \(\mathstrut -\mathstrut 495q^{54} \) \(\mathstrut -\mathstrut 165q^{55} \) \(\mathstrut +\mathstrut 176q^{56} \) \(\mathstrut -\mathstrut 176q^{57} \) \(\mathstrut -\mathstrut 286q^{58} \) \(\mathstrut +\mathstrut 77q^{59} \) \(\mathstrut +\mathstrut 539q^{60} \) \(\mathstrut +\mathstrut 297q^{61} \) \(\mathstrut +\mathstrut 385q^{62} \) \(\mathstrut +\mathstrut 264q^{63} \) \(\mathstrut +\mathstrut 341q^{64} \) \(\mathstrut +\mathstrut 220q^{65} \) \(\mathstrut +\mathstrut 264q^{66} \) \(\mathstrut +\mathstrut 11q^{67} \) \(\mathstrut -\mathstrut 66q^{69} \) \(\mathstrut -\mathstrut 198q^{70} \) \(\mathstrut -\mathstrut 176q^{71} \) \(\mathstrut -\mathstrut 638q^{72} \) \(\mathstrut -\mathstrut 121q^{73} \) \(\mathstrut -\mathstrut 352q^{74} \) \(\mathstrut +\mathstrut 154q^{75} \) \(\mathstrut +\mathstrut 110q^{76} \) \(\mathstrut +\mathstrut 110q^{77} \) \(\mathstrut +\mathstrut 759q^{78} \) \(\mathstrut +\mathstrut 33q^{79} \) \(\mathstrut -\mathstrut 242q^{80} \) \(\mathstrut +\mathstrut 737q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 154q^{83} \) \(\mathstrut +\mathstrut 11q^{84} \) \(\mathstrut +\mathstrut 275q^{85} \) \(\mathstrut +\mathstrut 143q^{86} \) \(\mathstrut +\mathstrut 517q^{87} \) \(\mathstrut +\mathstrut 429q^{88} \) \(\mathstrut +\mathstrut 121q^{89} \) \(\mathstrut +\mathstrut 242q^{90} \) \(\mathstrut -\mathstrut 110q^{92} \) \(\mathstrut -\mathstrut 286q^{93} \) \(\mathstrut -\mathstrut 352q^{94} \) \(\mathstrut -\mathstrut 154q^{95} \) \(\mathstrut -\mathstrut 440q^{96} \) \(\mathstrut +\mathstrut 154q^{97} \) \(\mathstrut +\mathstrut 77q^{98} \) \(\mathstrut -\mathstrut 242q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(23))\)

We only show spaces with odd 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
23.3.b \(\chi_{23}(22, \cdot)\) 23.3.b.a 3 1
23.3.d \(\chi_{23}(5, \cdot)\) 23.3.d.a 30 10