Properties

Label 5.34.b
Level 5
Weight 34
Character orbit b
Rep. character \(\chi_{5}(4,\cdot)\)
Character field \(\Q\)
Dimension 16
Newforms 1
Sturm bound 17
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 34 \)
Character orbit: \([\chi]\) = 5.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(17\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(5, [\chi])\).

Total New Old
Modular forms 18 18 0
Cusp forms 16 16 0
Eisenstein series 2 2 0

Trace form

\(16q \) \(\mathstrut -\mathstrut 72851326872q^{4} \) \(\mathstrut -\mathstrut 232168160280q^{5} \) \(\mathstrut +\mathstrut 11001777346872q^{6} \) \(\mathstrut -\mathstrut 27535156574590368q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut -\mathstrut 72851326872q^{4} \) \(\mathstrut -\mathstrut 232168160280q^{5} \) \(\mathstrut +\mathstrut 11001777346872q^{6} \) \(\mathstrut -\mathstrut 27535156574590368q^{9} \) \(\mathstrut -\mathstrut 22271193818331880q^{10} \) \(\mathstrut +\mathstrut 219974590742466912q^{11} \) \(\mathstrut -\mathstrut 10416043581549356184q^{14} \) \(\mathstrut +\mathstrut 9232415497377901440q^{15} \) \(\mathstrut +\mathstrut 133171456389985196576q^{16} \) \(\mathstrut -\mathstrut 2949217257058889591200q^{19} \) \(\mathstrut +\mathstrut 5571772909456424216760q^{20} \) \(\mathstrut +\mathstrut 20126160533851210892592q^{21} \) \(\mathstrut -\mathstrut 236696360036140740492000q^{24} \) \(\mathstrut +\mathstrut 269473151678676722148400q^{25} \) \(\mathstrut +\mathstrut 23043234216449373353232q^{26} \) \(\mathstrut +\mathstrut 2210824656972934579370400q^{29} \) \(\mathstrut -\mathstrut 7438800885032297852420760q^{30} \) \(\mathstrut +\mathstrut 4805180075928582021889472q^{31} \) \(\mathstrut -\mathstrut 106706080442140703440064q^{34} \) \(\mathstrut +\mathstrut 34840114703893102459924320q^{35} \) \(\mathstrut +\mathstrut 150609707516636111776170456q^{36} \) \(\mathstrut -\mathstrut 950668737676648885834065216q^{39} \) \(\mathstrut +\mathstrut 967967034953888345833396000q^{40} \) \(\mathstrut +\mathstrut 960625982433026021733974352q^{41} \) \(\mathstrut -\mathstrut 4300041994750366563328828704q^{44} \) \(\mathstrut +\mathstrut 5959973976670208219568382440q^{45} \) \(\mathstrut +\mathstrut 4030532465737707969346868392q^{46} \) \(\mathstrut -\mathstrut 48902999941413820155855454112q^{49} \) \(\mathstrut +\mathstrut 64132734499011351066825776400q^{50} \) \(\mathstrut +\mathstrut 37677263492556888574173469632q^{51} \) \(\mathstrut -\mathstrut 416785644990759180210455480400q^{54} \) \(\mathstrut +\mathstrut 208827421951347317583761567040q^{55} \) \(\mathstrut +\mathstrut 209868986171565551575474447200q^{56} \) \(\mathstrut -\mathstrut 204679212804521237512362904800q^{59} \) \(\mathstrut -\mathstrut 320542648209593925139588560480q^{60} \) \(\mathstrut -\mathstrut 62902839261738400132019069488q^{61} \) \(\mathstrut +\mathstrut 3273202940251902417009873735808q^{64} \) \(\mathstrut -\mathstrut 1155813780125630532662955267360q^{65} \) \(\mathstrut -\mathstrut 2991219624550267460630717491296q^{66} \) \(\mathstrut +\mathstrut 6899695112224183044828868241904q^{69} \) \(\mathstrut -\mathstrut 5880904834264312779374002982280q^{70} \) \(\mathstrut -\mathstrut 87525095316001019795902439808q^{71} \) \(\mathstrut +\mathstrut 43140282179597200538055251968176q^{74} \) \(\mathstrut -\mathstrut 27726088944293536006405507003200q^{75} \) \(\mathstrut -\mathstrut 38605994956626944020944749752800q^{76} \) \(\mathstrut -\mathstrut 10590745643822309766800662264000q^{79} \) \(\mathstrut +\mathstrut 24913342429758171577982759437920q^{80} \) \(\mathstrut +\mathstrut 126385893984816788804508532470336q^{81} \) \(\mathstrut -\mathstrut 401968339664232685914350670917664q^{84} \) \(\mathstrut +\mathstrut 174616747052458036927895334806720q^{85} \) \(\mathstrut -\mathstrut 18805496634715830052189508032488q^{86} \) \(\mathstrut -\mathstrut 816457769414638729740610145056800q^{89} \) \(\mathstrut +\mathstrut 814730708455223899676092744179240q^{90} \) \(\mathstrut +\mathstrut 572310345418666359618454810906752q^{91} \) \(\mathstrut +\mathstrut 1084618018208246129370832376900296q^{94} \) \(\mathstrut -\mathstrut 960346549067575215463879922304000q^{95} \) \(\mathstrut -\mathstrut 1376269400022374885061468958478208q^{96} \) \(\mathstrut +\mathstrut 3432482025669259323040953857901024q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{34}^{\mathrm{new}}(5, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5.34.b.a \(16\) \(34.491\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-232168160280\) \(0\) \(q+\beta _{1}q^{2}+(-52\beta _{1}+\beta _{3})q^{3}+(-4553207930+\cdots)q^{4}+\cdots\)