Properties

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

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
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

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

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

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 7 T^{3} + 64 T^{6} \))
$3$ (\( 1 + 38 T^{3} + 729 T^{6} \))
$5$ (\( ( 1 - 5 T )^{3}( 1 + 5 T )^{3} \))
$7$ (\( ( 1 - 7 T )^{3}( 1 + 7 T )^{3} \))
$11$ (\( ( 1 - 11 T )^{3}( 1 + 11 T )^{3} \))
$13$ (\( 1 - 1082 T^{3} + 4826809 T^{6} \))
$17$ (\( ( 1 - 17 T )^{3}( 1 + 17 T )^{3} \))
$19$ (\( ( 1 - 19 T )^{3}( 1 + 19 T )^{3} \))
$23$ (\( ( 1 + 23 T )^{3} \))
$29$ (\( 1 - 30746 T^{3} + 594823321 T^{6} \))
$31$ (\( 1 - 58754 T^{3} + 887503681 T^{6} \))
$37$ (\( ( 1 - 37 T )^{3}( 1 + 37 T )^{3} \))
$41$ (\( 1 - 43634 T^{3} + 4750104241 T^{6} \))
$43$ (\( ( 1 - 43 T )^{3}( 1 + 43 T )^{3} \))
$47$ (\( 1 + 205342 T^{3} + 10779215329 T^{6} \))
$53$ (\( ( 1 - 53 T )^{3}( 1 + 53 T )^{3} \))
$59$ (\( ( 1 - 26 T + 3481 T^{2} )^{3} \))
$61$ (\( ( 1 - 61 T )^{3}( 1 + 61 T )^{3} \))
$67$ (\( ( 1 - 67 T )^{3}( 1 + 67 T )^{3} \))
$71$ (\( 1 - 667154 T^{3} + 128100283921 T^{6} \))
$73$ (\( 1 - 725042 T^{3} + 151334226289 T^{6} \))
$79$ (\( ( 1 - 79 T )^{3}( 1 + 79 T )^{3} \))
$83$ (\( ( 1 - 83 T )^{3}( 1 + 83 T )^{3} \))
$89$ (\( ( 1 - 89 T )^{3}( 1 + 89 T )^{3} \))
$97$ (\( ( 1 - 97 T )^{3}( 1 + 97 T )^{3} \))
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