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Properties

Label 4.45
Level 4
Weight 45
Dimension 21
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 45
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 45 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(45\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{45}(\Gamma_1(4))\).

Total New Old
Modular forms 23 23 0
Cusp forms 21 21 0
Eisenstein series 2 2 0

Trace form

\( 21 q + 605612 q^{2} - 13046580445680 q^{4} - 1191857871142214 q^{5} - 151089021270839424 q^{6} + 96298933068226423232 q^{8} - 5759619100948009102011 q^{9} + O(q^{10}) \) \( 21 q + 605612 q^{2} - 13046580445680 q^{4} - 1191857871142214 q^{5} - 151089021270839424 q^{6} + 96298933068226423232 q^{8} - 5759619100948009102011 q^{9} - 12505573328866519603944 q^{10} - 1008582008803903346004480 q^{12} - 342266720642595008327526 q^{13} - 18812570969221737757007616 q^{14} - 429323192915437820302089984 q^{16} - 634801063423464784179430166 q^{17} - 3038124069658099834390851348 q^{18} - 95178771568328392075054272224 q^{20} + 25941411600333949914183048192 q^{21} + 727384969503500811258425746560 q^{22} - 6784766426651218183744450246656 q^{24} + 22093991393233408379523436028271 q^{25} + 53422584580753843254877931773336 q^{26} - 46674441078105565706123745254400 q^{28} - 172856649054100027513483366649510 q^{29} - 208471390136203333591535590099200 q^{30} + 3242792133809678876696622531894272 q^{32} + 7273361532485316304507716956536320 q^{33} - 13156262381829636429055579069468584 q^{34} - 33874660869572147385235178078305008 q^{36} - 16356933662060836651930347592620486 q^{37} + 45856687255867991685965015678509440 q^{38} - 483040727182327173950693008664191104 q^{40} + 211290721897052900032957839223418122 q^{41} + 409589852913664867740496861674209280 q^{42} + 3339472512955444037822475478956188160 q^{44} + 2039093001210970787360916299316874266 q^{45} - 5806749290972389592256524077295633664 q^{46} - 5340253533684189604832993455433195520 q^{48} - 43299262012369466157823154150393550411 q^{49} + 28288224613316806931187340605385090116 q^{50} - 109456821928895615986497840386233526496 q^{52} - 124060719819939466178716849900255596806 q^{53} + 85603264604984031892020748836682460928 q^{54} + 311261017039966191188280314622394331136 q^{56} + 406929883110207715079424916765543918080 q^{57} - 2126008932920829662698391859008777819496 q^{58} - 372686235229043362754072188852707148800 q^{60} + 309426872572239588043263812927207839962 q^{61} + 1156322127848885203066778833646710993920 q^{62} - 4902730151741626597806839009324881735680 q^{64} - 13492158093033658477402057894275487889068 q^{65} + 24932659300030021765520575242010626293760 q^{66} - 3916274595737468444125500208547201271776 q^{68} + 2565337248483798670232893328361624695808 q^{69} - 98879252613169806434542823461625902886400 q^{70} + 147302554284819254485927378700631841025472 q^{72} + 147531457140172751132283617562594502945674 q^{73} + 290171560916431669411259551792076861277976 q^{74} - 43184981979196571535874879172681105164800 q^{76} + 446394181490740211970215422489995719377920 q^{77} - 964200119976088262334169600001693579520 q^{78} - 2011490663947381735501612576922685486493184 q^{80} - 2178726246184026497923052568920748979977867 q^{81} - 1150958323935947560362508440440048448874536 q^{82} + 6209941380868192540343252076606108902719488 q^{84} + 5679851477841926148420178187348291823631092 q^{85} - 2915338479242605399415746860762643287652224 q^{86} + 705030880368125854811890748326710823188480 q^{88} - 27170409944693321104174610773080947078942390 q^{89} + 12369354273355664792550176907847193877155736 q^{90} - 27540241567678746217506869357458705431966720 q^{92} + 41096485388187686620928799812891400047800320 q^{93} + 15862476520232897460465561775346899863780864 q^{94} - 34622322558806891728108279325640392329887744 q^{96} - 108718469585945280803765850286496694817884246 q^{97} - 102805093097570330181433576830227627173185748 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{45}^{\mathrm{new}}(\Gamma_1(4))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
4.45.b \(\chi_{4}(3, \cdot)\) 4.45.b.a 1 1
4.45.b.b 20