Properties

Label 4.23.b
Level 4
Weight 23
Character orbit b
Rep. character \(\chi_{4}(3,\cdot)\)
Character field \(\Q\)
Dimension 10
Newforms 1
Sturm bound 11
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 23 \)
Character orbit: \([\chi]\) = 4.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 4 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(11\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{23}(4, [\chi])\).

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

Trace form

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

Decomposition of \(S_{23}^{\mathrm{new}}(4, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4.23.b.a \(10\) \(12.268\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(1540\) \(0\) \(-17091100\) \(0\) \(q+(154-\beta _{1})q^{2}+(-19\beta _{1}-\beta _{2})q^{3}+\cdots\)