Properties

Label 5.18.a
Level 5
Weight 18
Character orbit a
Rep. character \(\chi_{5}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 2
Sturm bound 9
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 18 \)
Character orbit: \([\chi]\) = 5.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(9\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(5))\).

Total New Old
Modular forms 9 5 4
Cusp forms 7 5 2
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(5\)Dim.
\(+\)\(2\)
\(-\)\(3\)

Trace form

\(5q \) \(\mathstrut +\mathstrut 798q^{2} \) \(\mathstrut +\mathstrut 4964q^{3} \) \(\mathstrut +\mathstrut 87060q^{4} \) \(\mathstrut +\mathstrut 390625q^{5} \) \(\mathstrut -\mathstrut 11408840q^{6} \) \(\mathstrut -\mathstrut 20681392q^{7} \) \(\mathstrut +\mathstrut 68510280q^{8} \) \(\mathstrut +\mathstrut 399234265q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut +\mathstrut 798q^{2} \) \(\mathstrut +\mathstrut 4964q^{3} \) \(\mathstrut +\mathstrut 87060q^{4} \) \(\mathstrut +\mathstrut 390625q^{5} \) \(\mathstrut -\mathstrut 11408840q^{6} \) \(\mathstrut -\mathstrut 20681392q^{7} \) \(\mathstrut +\mathstrut 68510280q^{8} \) \(\mathstrut +\mathstrut 399234265q^{9} \) \(\mathstrut -\mathstrut 219531250q^{10} \) \(\mathstrut +\mathstrut 736392060q^{11} \) \(\mathstrut -\mathstrut 847383152q^{12} \) \(\mathstrut +\mathstrut 3777271134q^{13} \) \(\mathstrut -\mathstrut 2072144880q^{14} \) \(\mathstrut +\mathstrut 10517187500q^{15} \) \(\mathstrut -\mathstrut 10554171120q^{16} \) \(\mathstrut +\mathstrut 17882253978q^{17} \) \(\mathstrut -\mathstrut 59413475866q^{18} \) \(\mathstrut -\mathstrut 22990074300q^{19} \) \(\mathstrut -\mathstrut 20792187500q^{20} \) \(\mathstrut +\mathstrut 151444770360q^{21} \) \(\mathstrut -\mathstrut 743329560344q^{22} \) \(\mathstrut +\mathstrut 88453643904q^{23} \) \(\mathstrut +\mathstrut 167744704800q^{24} \) \(\mathstrut +\mathstrut 762939453125q^{25} \) \(\mathstrut +\mathstrut 3413941773060q^{26} \) \(\mathstrut +\mathstrut 1134753193880q^{27} \) \(\mathstrut -\mathstrut 2958913603744q^{28} \) \(\mathstrut -\mathstrut 6717877568250q^{29} \) \(\mathstrut +\mathstrut 2566684375000q^{30} \) \(\mathstrut +\mathstrut 4091066362160q^{31} \) \(\mathstrut -\mathstrut 13601229092832q^{32} \) \(\mathstrut +\mathstrut 12219974135008q^{33} \) \(\mathstrut -\mathstrut 11754816868580q^{34} \) \(\mathstrut +\mathstrut 9750003125000q^{35} \) \(\mathstrut +\mathstrut 26904710046980q^{36} \) \(\mathstrut +\mathstrut 7200734791318q^{37} \) \(\mathstrut -\mathstrut 73963660327080q^{38} \) \(\mathstrut -\mathstrut 49577437276120q^{39} \) \(\mathstrut +\mathstrut 24058828125000q^{40} \) \(\mathstrut -\mathstrut 58639248237990q^{41} \) \(\mathstrut +\mathstrut 368236786390176q^{42} \) \(\mathstrut +\mathstrut 39049006404444q^{43} \) \(\mathstrut -\mathstrut 223407642299280q^{44} \) \(\mathstrut +\mathstrut 97090083203125q^{45} \) \(\mathstrut -\mathstrut 290381341303440q^{46} \) \(\mathstrut +\mathstrut 560714665635288q^{47} \) \(\mathstrut -\mathstrut 542741018933696q^{48} \) \(\mathstrut -\mathstrut 362339446450315q^{49} \) \(\mathstrut +\mathstrut 121765136718750q^{50} \) \(\mathstrut -\mathstrut 520804419046040q^{51} \) \(\mathstrut +\mathstrut 1823362047940888q^{52} \) \(\mathstrut -\mathstrut 435506791917786q^{53} \) \(\mathstrut -\mathstrut 2780356593846800q^{54} \) \(\mathstrut +\mathstrut 1110587098437500q^{55} \) \(\mathstrut -\mathstrut 1181635449432000q^{56} \) \(\mathstrut +\mathstrut 6130627916698160q^{57} \) \(\mathstrut -\mathstrut 979293205423420q^{58} \) \(\mathstrut -\mathstrut 5235706577006100q^{59} \) \(\mathstrut +\mathstrut 2762398956250000q^{60} \) \(\mathstrut +\mathstrut 3286542037858110q^{61} \) \(\mathstrut +\mathstrut 5500522387896576q^{62} \) \(\mathstrut -\mathstrut 7978269996483936q^{63} \) \(\mathstrut -\mathstrut 7129329294639040q^{64} \) \(\mathstrut +\mathstrut 2754735333593750q^{65} \) \(\mathstrut +\mathstrut 1922942936973920q^{66} \) \(\mathstrut +\mathstrut 3291302147555828q^{67} \) \(\mathstrut -\mathstrut 1888622336311704q^{68} \) \(\mathstrut -\mathstrut 14634062044658520q^{69} \) \(\mathstrut +\mathstrut 9018160743750000q^{70} \) \(\mathstrut -\mathstrut 3908528312372040q^{71} \) \(\mathstrut +\mathstrut 22930402491977640q^{72} \) \(\mathstrut -\mathstrut 1147634674990446q^{73} \) \(\mathstrut -\mathstrut 12290576220737580q^{74} \) \(\mathstrut +\mathstrut 757446289062500q^{75} \) \(\mathstrut -\mathstrut 7199023263782000q^{76} \) \(\mathstrut +\mathstrut 10970815186652976q^{77} \) \(\mathstrut -\mathstrut 22136761293403952q^{78} \) \(\mathstrut +\mathstrut 6574063045463600q^{79} \) \(\mathstrut -\mathstrut 8536417493750000q^{80} \) \(\mathstrut +\mathstrut 4212399493253605q^{81} \) \(\mathstrut -\mathstrut 14844458017154164q^{82} \) \(\mathstrut +\mathstrut 66630532639512324q^{83} \) \(\mathstrut +\mathstrut 92716763018517120q^{84} \) \(\mathstrut -\mathstrut 28393305430468750q^{85} \) \(\mathstrut -\mathstrut 35605762154942040q^{86} \) \(\mathstrut -\mathstrut 93965064890397160q^{87} \) \(\mathstrut +\mathstrut 32201422365176160q^{88} \) \(\mathstrut +\mathstrut 29920202439689250q^{89} \) \(\mathstrut -\mathstrut 88312627541406250q^{90} \) \(\mathstrut -\mathstrut 31464894738701840q^{91} \) \(\mathstrut -\mathstrut 153380249446363872q^{92} \) \(\mathstrut -\mathstrut 7723516209480432q^{93} \) \(\mathstrut +\mathstrut 232113759527293120q^{94} \) \(\mathstrut -\mathstrut 14423068867187500q^{95} \) \(\mathstrut +\mathstrut 121678443767135360q^{96} \) \(\mathstrut -\mathstrut 229317165133259462q^{97} \) \(\mathstrut +\mathstrut 96345875569324686q^{98} \) \(\mathstrut +\mathstrut 201782836863719180q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(5))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5
5.18.a.a \(2\) \(9.161\) \(\Q(\sqrt{39}) \) None \(680\) \(-10980\) \(-781250\) \(-22820700\) \(+\) \(q+(340+\beta )q^{2}+(-5490-52\beta )q^{3}+\cdots\)
5.18.a.b \(3\) \(9.161\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(118\) \(15944\) \(1171875\) \(2139308\) \(-\) \(q+(39-\beta _{1})q^{2}+(5317+8\beta _{1}+\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(5))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(5)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)