Properties

Label 4.23
Level 4
Weight 23
Dimension 10
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 23
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 23 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(23\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{23}(\Gamma_1(4))\).

Total New Old
Modular forms 12 12 0
Cusp forms 10 10 0
Eisenstein series 2 2 0

Trace form

\( 10 q + 1540 q^{2} + 2264464 q^{4} - 17091100 q^{5} - 791935776 q^{6} + 9804431680 q^{8} - 104309613702 q^{9} + O(q^{10}) \) \( 10 q + 1540 q^{2} + 2264464 q^{4} - 17091100 q^{5} - 791935776 q^{6} + 9804431680 q^{8} - 104309613702 q^{9} + 159414035240 q^{10} + 519021175680 q^{12} - 531230356540 q^{13} - 5894008940736 q^{14} - 27717620084480 q^{16} + 14058178115540 q^{17} + 16283956279140 q^{18} + 233643631625120 q^{20} - 313135665760512 q^{21} + 120589650366240 q^{22} - 2007619616180736 q^{24} + 7710175817606670 q^{25} - 3953973318046744 q^{26} + 1177952265288960 q^{28} - 14464474185570172 q^{29} + 10252783730669760 q^{30} - 73831192092953600 q^{32} + 72906957628179840 q^{33} - 26625976920357496 q^{34} - 36609276067793136 q^{36} + 324587767823538020 q^{37} + 369140808808591200 q^{38} - 1158049295468479360 q^{40} - 1355457345814233100 q^{41} + 2644455724909770240 q^{42} - 1919761520625210240 q^{44} + 9367295763131460 q^{45} + 6132624002565203904 q^{46} - 18374169355003791360 q^{48} + 183553700661552298 q^{49} + 29084394113996178540 q^{50} - 38492433127521128800 q^{52} - 11424344766226018780 q^{53} + 79182840955393027008 q^{54} - 102844865827678657536 q^{56} + 30188516183231506560 q^{57} + 173059696836432320360 q^{58} - 377769459746631548160 q^{60} + 58241718146183220740 q^{61} + 317897221476923285760 q^{62} - 412080172429987966976 q^{64} - 121531695066047433560 q^{65} + 700585278654050000640 q^{66} - 667890522330713878240 q^{68} + 54497497397908094208 q^{69} + 1014396282552321513600 q^{70} - 1244773253376491901120 q^{72} + 83030422224875883380 q^{73} + 801906083011176262184 q^{74} + 286747421140990627200 q^{76} - 704201825495570814720 q^{77} - 964412732782594923840 q^{78} + 1509611955050789726720 q^{80} + 251577744224553978858 q^{81} - 2389572513290905036600 q^{82} + 6185640644326191863808 q^{84} - 1796890366112110859960 q^{85} - 8221838255181360278496 q^{86} + 11178210842814940531200 q^{88} + 3420669206528505615668 q^{89} - 24782809563337507735320 q^{90} + 21476264197983864733440 q^{92} + 15493754050318100597760 q^{93} - 20874543047091388369536 q^{94} + 29250284502468708163584 q^{96} - 20429910746446196146540 q^{97} - 23110416876469762175420 q^{98} + O(q^{100}) \)

Decomposition of \(S_{23}^{\mathrm{new}}(\Gamma_1(4))\)

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
4.23.b \(\chi_{4}(3, \cdot)\) 4.23.b.a 10 1