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Properties

Label 23.12
Level 23
Weight 12
Dimension 229
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 528
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(528\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(23))\).

Total New Old
Modular forms 253 249 4
Cusp forms 231 229 2
Eisenstein series 22 20 2

Trace form

\( 229 q + 37 q^{2} - 515 q^{3} + 2933 q^{4} - 9671 q^{5} + 12085 q^{6} + 33477 q^{7} - 168971 q^{8} + 227275 q^{9} + O(q^{10}) \) \( 229 q + 37 q^{2} - 515 q^{3} + 2933 q^{4} - 9671 q^{5} + 12085 q^{6} + 33477 q^{7} - 168971 q^{8} + 227275 q^{9} + 231829 q^{10} - 1069235 q^{11} + 741877 q^{12} + 1155465 q^{13} - 803723 q^{14} + 16841090 q^{15} - 36689931 q^{16} + 26284284 q^{17} + 54358373 q^{18} - 43078882 q^{19} - 99817227 q^{20} + 57241378 q^{21} + 139041258 q^{22} + 39655991 q^{23} - 384485398 q^{24} - 169269939 q^{25} - 105922603 q^{26} + 537374080 q^{27} + 815014901 q^{28} - 235600992 q^{29} - 1371677707 q^{30} - 215032414 q^{31} + 1658202101 q^{32} - 150749872 q^{33} + 1323737099 q^{34} + 334103279 q^{35} - 5339262998 q^{36} + 202980629 q^{37} + 5468956064 q^{38} + 3537025225 q^{39} - 3169251811 q^{40} - 3134154073 q^{41} - 12625276205 q^{42} - 705435103 q^{43} + 10168800836 q^{44} + 13276647608 q^{45} + 12956555885 q^{46} - 5777131442 q^{47} - 17442626979 q^{48} - 16040102171 q^{49} - 18518884686 q^{50} + 4425731449 q^{51} + 34617848447 q^{52} + 14130088391 q^{53} + 34044228909 q^{54} + 2214659731 q^{55} - 81253343842 q^{56} - 65440818278 q^{57} + 22609889236 q^{58} + 80534887995 q^{59} + 74338508039 q^{60} + 2236714181 q^{61} - 28768143563 q^{62} - 57148221930 q^{63} - 96658259979 q^{64} - 37034195734 q^{65} + 29977549356 q^{66} + 54245371711 q^{67} + 171588161258 q^{68} + 63248326800 q^{69} + 33391303146 q^{70} - 58656805410 q^{71} - 208319930324 q^{72} - 50251439609 q^{73} - 314753258896 q^{74} + 238030441872 q^{75} + 264864092306 q^{76} + 33531466148 q^{77} - 233128774741 q^{78} - 45176151011 q^{79} + 99140610170 q^{80} + 350223060515 q^{81} + 7273356135 q^{82} + 33232473396 q^{83} + 68715742659 q^{84} - 147433250279 q^{85} - 724650207877 q^{86} - 550866858047 q^{87} - 181852674531 q^{88} + 195206771323 q^{89} + 1007375137222 q^{90} + 529800997522 q^{91} + 576224023366 q^{92} + 409924761326 q^{93} + 27890542140 q^{94} - 786189794390 q^{95} - 701708875764 q^{96} - 476354983332 q^{97} - 1059162784835 q^{98} - 894469331906 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(23))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
23.12.a \(\chi_{23}(1, \cdot)\) 23.12.a.a 8 1
23.12.a.b 11
23.12.c \(\chi_{23}(2, \cdot)\) 23.12.c.a 210 10

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(23))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(23)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)