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Properties

Label 5.18.a
Level $5$
Weight $18$
Character orbit 5.a
Rep. character $\chi_{5}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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 and the Fricke involution.

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

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(5))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5
5.18.a.a 5.a 1.a $2$ $9.161$ \(\Q(\sqrt{39}) \) None \(680\) \(-10980\) \(-781250\) \(-22820700\) $+$ $\mathrm{SU}(2)$ \(q+(340+\beta )q^{2}+(-5490-52\beta )q^{3}+\cdots\)
5.18.a.b 5.a 1.a $3$ $9.161$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(118\) \(15944\) \(1171875\) \(2139308\) $-$ $\mathrm{SU}(2)$ \(q+(39-\beta _{1})q^{2}+(5317+8\beta _{1}+\beta _{2})q^{3}+\cdots\)

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

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