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

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

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