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

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

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

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