Properties

Label 5.12.a
Level 5
Weight 12
Character orbit a
Rep. character \(\chi_{5}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 6
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 5.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(5))\).

Total New Old
Modular forms 7 3 4
Cusp forms 5 3 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.
\(+\)\(2\)
\(-\)\(1\)

Trace form

\( 3q + 14q^{2} - 1012q^{3} + 6084q^{4} - 3125q^{5} + 33256q^{6} + 40344q^{7} - 346200q^{8} + 429271q^{9} + O(q^{10}) \) \( 3q + 14q^{2} - 1012q^{3} + 6084q^{4} - 3125q^{5} + 33256q^{6} + 40344q^{7} - 346200q^{8} + 429271q^{9} + 168750q^{10} - 1086964q^{11} - 1220576q^{12} + 3040218q^{13} + 737568q^{14} - 1787500q^{15} + 4433808q^{16} - 2406346q^{17} + 2755958q^{18} + 4945860q^{19} - 24587500q^{20} + 17740536q^{21} - 105430632q^{22} + 26485848q^{23} + 201348480q^{24} + 29296875q^{25} - 93479164q^{26} - 242961400q^{27} + 179345712q^{28} + 163837090q^{29} - 272225000q^{30} + 415992096q^{31} - 476025056q^{32} - 70979744q^{33} + 318732348q^{34} - 235800000q^{35} - 219085612q^{36} - 270337326q^{37} + 928850600q^{38} - 327962728q^{39} + 457125000q^{40} - 554400074q^{41} + 1902541008q^{42} - 1129907292q^{43} + 175433008q^{44} + 1471759375q^{45} - 1571769984q^{46} + 221408384q^{47} - 5130637952q^{48} - 3610791021q^{49} + 136718750q^{50} + 5250194296q^{51} + 13174967064q^{52} + 493431938q^{53} - 16555690640q^{54} + 466837500q^{55} - 2235656160q^{56} + 5021442800q^{57} + 9757106100q^{58} + 8243084780q^{59} + 8229700000q^{60} - 12415015014q^{61} - 22735073952q^{62} - 10750886232q^{63} + 9182013504q^{64} - 11838443750q^{65} + 9648059072q^{66} + 19529964204q^{67} - 1251711608q^{68} + 19869613032q^{69} - 6035550000q^{70} + 9971527816q^{71} - 63347763000q^{72} - 20102028402q^{73} + 58862619508q^{74} - 9882812500q^{75} - 986914320q^{76} - 26504706672q^{77} + 120428573776q^{78} - 24071709360q^{79} - 23679550000q^{80} + 47602946083q^{81} - 68124845412q^{82} + 16503964428q^{83} - 28385169792q^{84} - 15756956250q^{85} - 116541245224q^{86} - 21134853400q^{87} - 33934826400q^{88} + 50501550270q^{89} + 87037493750q^{90} + 97204540416q^{91} + 232124189904q^{92} - 301987859184q^{93} - 5091788112q^{94} - 17827437500q^{95} - 14295226624q^{96} + 123413770134q^{97} + 73456940302q^{98} - 92309175748q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(5))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5
5.12.a.a \(1\) \(3.842\) \(\Q\) None \(34\) \(-792\) \(3125\) \(-17556\) \(-\) \(q+34q^{2}-792q^{3}-892q^{4}+5^{5}q^{5}+\cdots\)
5.12.a.b \(2\) \(3.842\) \(\Q(\sqrt{151}) \) None \(-20\) \(-220\) \(-6250\) \(57900\) \(+\) \(q+(-10+3\beta )q^{2}+(-110+2^{4}\beta )q^{3}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(5))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(5)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)